Our back door on our 2007 Toyota Sienna will not stay closed. It will open automatically when we hit the remote. It will go all the up, then it comes right back down.

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Sometimes the lock on the handle from the interior gets stuck half way in/ out. Check its position. Mine does this periodically and then won't close, keeps opening. Also verify child safety close switch is in correct position.

I unlocked all doors, trans in park and it seemed to stay shut.

can it open manual? if it can see if there is any deb re inside the door latch, if so blow out with air gun and apply WD-40, let me know if that helped!
good luck!

Could be resistance in one of the tracks, or the motor.
If the motor hits a resistance the door opens in case the resistance is a human.

Open the inside panel of the door by popping off the little white clips holding it on. The cable connected to the inside release button is either caught on something or has come lose. Check out this video - https://www.youtube.com/watch?v=MkC2OiOiE_U

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.

http://www.findonefindall.com/toyota-sienna/siennareardoor.htm
pls check the given link and u ll find the procedure to unlock the back hatch

Here is what I have had success doing. Open the rear door, put a little grease on shock's inner rod, close the rear door to lubricate the shock internally. It may require a little more lubrication if it does not work the first time.