Can Pistons Move Obsidian?

When extending, sticky pistons act exactly as regular pistons, pushing up to 12 blocks. Although, when retracting, sticky pistons will pull along the block immediately in front of them. obsidian, bedrock, tile entities, and extended pistons cannot be pulled, just as they cannot be pushed.

What blocks can Pistons not move?

Some blocks cannot be pushed by pistons and the piston head will not extend. These blocks include Obsidian, Bedrock, Furnaces, Chests, etcetera. Pistons will not push blocks into the Void or the top of the map. Pumpkins, Cobwebs, Dragon Egg and Jack-O-Lanterns are turned back into items when pushed.

What can move obsidian?

The only ways to move obsidian are mining and placing or with commands, which probably aren't what you were thinking of.