I have similar space issues, and health concerns. I just throw an old shower curtain on the living room floor and clean the whole bike with dish washing liquid (mild degreaser) and water. I ride every day and I've been doing this for years. It's worked well for me. Harsher solvents might speed up the job, but they've been unnecessary for me.
The chain can be cleaned with the same dish washing liquid and water, rinsed clean with water, and re-oiled. I use a Park Tool CG-2 to make the process a little easier. An old toothbrush is useful too.