Doors dontopen or close using two rear buttons

Check for sticking mechanism. See if the Owner's Manual mentions LUBRICATING the door. Buy some graphite or teflon-type lubricating liquid to apply to mechanism. And I'd NOT use the electronic button until you get this fixed as you may burn-out / wear-out the motor prematurely.

The proper way would be to look at a wiring diagram an test the electrical circuit's with a DVOM - digital volt ohm meter . Do you know how to test automotive electrical circuit's ?
Electric Testing Techniques You Need to Know
The Trainer 32 How To Read An Automotive Block Wiring Diagram
Free wiring diagrams here http://www.bbbind.com/free_tsb.html
Enter the vehicle info. year , make model and engine size . Under system click on body & accessories ,then under subsystem click on power sliding door . Click the search button then the blue link. Looking at the diagram you will see a control module is used .
Also reading factory service info. on how it works would be a good idea.

Rear Side Door Actuator Control Module
The rear side door actuator control module is capable of on-board diagnostic functions described in On-Board Diagnostic Features . The rear side door actuator control module monitors the door position at all times including during manual operation. After activating the on-board diagnostic modes, loosing battery voltage, or ground to the rear side door actuator control module the Power Sliding Door (PSD) Re-Initialization procedure must be performed in order for the rear side door actuator control module to correctly determine the door position.
Power Sliding Door System Description
The power sliding door system(s) can operate correctly only if the power sliding door is in proper mechanical condition. Any mechanical problems will affect the power sliding door operation and must be repaired before attempting to diagnose the power sliding door system. Manually open and close the power sliding door to determine if the door moves smoothly and without excessive resistance or binding. The power sliding door must also latch and unlatch without the use of excessive force. At any time during power sliding door open or close operation, excessive resistance to the door movement will cause the power sliding door to stop and reverse the direction of travel.
The power sliding door will operate only when the power sliding door on/off switch in the overhead console is in the on position. At anytime during power sliding door operation the on/off switch may be turned to the off position and the system will quit any function in process. The power sliding door will not open unless the transmission shift lever is in the park position and the door is unlocked. When the sliding door security lock is in the locked position the power sliding door will not open from the inside. The power sliding door close function will operate when the vehicle is in gear. The power sliding door module uses the VSS signal to determine if the vehicle is moving during a power sliding door close function. The momentum of the vehicle moving forward adds resistance to the door closing operation. When the rear side door actuator control module determines the vehicle is moving forward while closing the door, current flow through the actuator motor is increased instead of being reversed. The VSS signal circuit is supplied battery positive voltage through a resistor then monitored within the rear side door actuator control module. The VSS signal circuit is then pulsed to ground, or pulled low by the powertrain control module in relation to vehicle speed. The sliding door alarm will sound repeated short tones whenever the power sliding door system is turned on and the door is open while the transmission is out of park.
When the power sliding door system is on and manual operation of the power sliding door is detected the rear side door actuator control module activates the power assist feature. When the power assist is activated the power sliding door will continue to open or close without any further manual effort.
The power sliding doors may be operated using the Remote Keyless Entry System. The keyless entry transmitter will have one OPEN/CLOSE button with a van symbol on it for each power sliding door. The power sliding door ON/OFF switches in the overhead console must be in the ON position in order to operate the power sliding doors using the keyless entry transmitter. When a right hand power sliding door OPEN/CLOSE function is activated using a keyless entry transmitter the exterior lights will flash once indicating the RKE module has received the OPEN/CLOSE command. When activating a left hand power sliding door OPEN/CLOSE function with the keyless entry transmitter the exterior lights will not flash.

On-Board Diagnostic Features
The left and right power sliding door systems operate as independent systems. The on-board diagnostic modes are entered and operate the same in both systems.
The power sliding door systems are capable of the following on-board diagnostic functions:
• Diagnostic Mode 1: An audible signal indicates the diagnostic trouble codes stored by the rear side door actuator control module.
• Diagnostic Mode 2: An audible signal indicates when inputs to the rear side door actuator control module are active.
• Diagnostic Mode 3: Performs an output test of the sliding door unlatch actuator.
Entering On-Board Diagnostics
The on-board diagnostic modes can only be entered in a sequential order from modes 1-3.
• Enter the right power sliding door system on-board diagnostics using the right B-pillar open/close switch and the right on/off switch in the overhead console.
• Enter the left power sliding door system on-board diagnostics using the left B-pillar open/close switch and the left on/off switch in the overhead console.
1. Both power sliding doors must be closed and in the latched position.
2. Place the ignition switch in the OFF position.
3. Place the on/off switch in the overhead console to the OFF position.
4. Press and hold the B-pillar power sliding door open/close switch.
5. While holding the open/close switch, operate the on/off switch through 10 ON and OFF cycles within 10 seconds stopping in the on position.
6. The sliding door alarm will sound 1 long tone indicating diagnostic mode 1 is active.
Diagnostic Mode 1
Upon activating diagnostic mode 1, DTCs will begin to be signaled by the sliding door alarm. The DTCs are 2 digit codes and the codes are represented by the number of buzzes for each digit of the code number. For example a DTC 12 is represented with the following sequence: buzz, pause, buzz, buzz, long pause. Each DTC will be signaled 3 times before proceeding to the next DTC. Refer to Diagnostic Trouble Code (DTC) List . The DTCs will continue to be repeated in this manner until the on-board diagnostics are exited or mode 2 is entered. When exiting the on-board diagnostics all stored DTCs will be erased from the rear side door actuator control module memory.

I'm not sure about the noise, but the jerking motion might be because your the center roller (located in the rear middle of the sliding door) has worn out and need to be replace. This is a will known problem.

Your problem is very hard to answer because 05-10 odyssey has so many problem with sliding door.

rear latch:
-door not to latch close
-door not to work

front latch:
-door not to open

lock actuator:
-door not to open
-door will pop when opening

window motor:
-window not to work
-door will only open half way

center roller:
-jerking motion when opening
-door kick back close while opening
-door kick back open while closing

Door motor:
-door not to work
-cause door to jam

good luck

Did you check the button that you can accidently switch on the inside of the glove box? It controls the motor that opens the power back door.

This may or may not work depending on exactly what is wrong with the door, I cant tell what is wrong without looking at it directly however:
You can try starting with all doors closed and unlocked, keys in hand disconnecting the battery and letting the vehicle sit for 2 min or so, then reconnect the battery. Put the key into the ignition and turn it to the on position but do not start the van. Next press the button to disable the power sliding door for the drivers side, then manually open the door fully, wait 5 seconds, then close it manually fully. Press button the button again to re-enable the power sliding door, then try to use it with the automatic feature either by pulling the handle or using your remote, this may or may not work depending on if the door has somehow become de-initialized (it should work now) however if something is broken inside the door closing mechanism or door closed/open sensors, the door will continue to malfunction.

If it will not open or close using the remote and all other functions of the rmote work then it is likely to be the remote receiver inside the door behind the door liner. If it will not open or close using the handles the coupler may not be fastened that goes to the motor behind the right side liner. Or the motor may be bad. If you turn the doors off using the switch at the drivers left side and they still won't open or close check to see if the door is still on the rollers and not jammed up. The power motor may have gone bad or it may need to have the cable tension adjusted.

Look in your owners manual there is a procedure to reset the door controls. If that dosen't work maybe the motor is burnt out, it's in the left rear access panel.

Something similar to that was happening with our Odyssey...the beeping when you are driving whether it's ongoing or intermittent is the "safety alarm" letting you know the door is not closed. The power lock is not engaging. What I do when I get the beeping while driving is hit the Door Close button. It causes the door to attempt to engage again. To fix it...we first cleaned out the space below the side running board (kids were hiding crayons and things in there), then looked for any obstructions along the top and bottom tracks. I sprayed a lubricant along the tracks (I'd suggest the dry lube kind...I used WD40 the 1st time and had streaks of it dripping down after driving), use a lube that has a long straw to spray in small places...and spray up into the track that runs the length of the middle of the car. Manually open and shut it a few times to get the tracks lubed, then try it out.
If you press the open OR close button by remote or in the car and get nothing...no movement/no noises/no beeping...then it could be the electrical circuit itself, the signal itself may be impeded...or the motor shot. Have you tried any of these suggestions before?

there is a cable of wires that lay in the track under the slider they break from normal use.. the harness it fairly easy to change.. when you open the door lok in the opening you will see the harness there in black plastic

sounds like the child safty lock is on you can find it by looking in your book for your car