Can I repair the floor in the water heater closet with an old street sign?
Can I use an old aluminum road sign as a replacement floor for my hot
  water heater closet?


I'm sorry, but that made me laugh.

First thing you should do, is find what is causing the floor to rot and fix the leak.  What is "spongy"?  The floor or the joist?  If the joists are rotten, you need to replace them, then put a new floor down.

After you fix the leak problem and install a new floor, you could install a Water Heater Drain Pan under your water heater, which will catch any leaking water and drain it away (with the proper plumbing hookups)