It's handy to have a hot water connection in the laundry room. :-) I connected a hose and used it to wash away the engine degreaser, and used the shop vac to collect the water as I went. Then, I washed it again with Pine Sol. The result was no greasy residue whatsoever - I was impressed with how well it worked.
Unfortunately the house smelled like engine degreaser all night, and we had to leave some windows open even with the freezing weather. In these rooms I also opened the windows, closed the doors (to keep the cold out of the rest of the house somewhat) and left a fan running to try to exhaust the fumes. The furnace had to work hard that night.