if i equip my opponents monster with Snatch Steal, then i activate giant Trunade, will my opponents monster return to his side of the field or stay on mine?

Yes...it returns to the opponent's side since it is face-up and no longer equipped...which is what is required to keep control...

The ONLY way right now to keep control of a monster taken control of by Snatch Steal is to flip it face-down while it's still equipped.

what about removing the monster from play, say with Interdimenssionall meatter Transporter? once it comes back would it come back to my side of the field or his?

It would return to your side, but then immediately return to the owner's side of the field...as I stated above...

"The ONLY way right now to keep control of a monster taken control of by Snatch Steal is to flip it face-down while it's still equipped."

i think what you are looking for is book of moon. snatch your opponents monster. play trunade and chain it with book of moon and flip the snatched monster face down. but i believe snatch would go to the grave still.

Yep...as soon as the monster goes f/d, game mechanics will destroy Snatch Steal and send it to the Graveyard. If any equips with secondary effects (like Axe of Despair, Malevolant Nuzzler, Horn of Light and such) are sent to the Graveyard, they activate after the chain fully resolves.