I have a small bucket filled with sawdust that I use to store used cooking oil. Bucket stays in the garage as it'll eventually go rancid. When it does, it gets thrown into the trash. The resulting mess is still greasy, but not runny. The key here is that soaking it this way limits the mess that can happen if it's knocked over; sawdust is what you use to clean an oil spill anyway.

Wood-based cat litter would also work for this. It's just compressed sawdust pellets^1^.

Edit: I have not looked into donating it as biodiesel. That would probably be a somewhat more green option.

^1^ - very likely made in the same fashion as pellet stove fuel, so that might work too.