Worst possible timing.l.

I just submitted my indefinite leave to remain paperwork on March 14th, including of course, my passport and visa.  I believe I may lose my job on Friday.  Now I'll be looking for work, but don't have my passport/visa showing the right to work.  What can I do?  Actually, my visa expired on March 15th, so that won't even help until my indefinite leave is approved.  Do I even have the right to work?

You're kind of between a rock and a hard place, unfortunately.  You are covered by the terms of your previous visa while your ILR is being processed/decided so technically you are allowed to work but without the proof of a visa to show a potential employer they are not going to be able to hire you. 

Do you have a scan or copy of your visa page anywhere? Does your job? It might be worth getting a copy if they do. How frustrating!

The Home Office has an employer checking service for this purpose:

http://www.ukba.homeoffice.gov.uk/business-sponsors/preventing-illegal-working/support/ecs/