Of course, without testing, there is no sure-fire way to tell what strength it is, but here is my educated guess:

Reinforcing steel of that era would have most likely been grade 33, 40, or 50 (ksi yield strengths).  My guess is grade 40 for a building in the 1950's.

Welded wire mesh is a little harder.  I think it depends on whether the mesh is smooth wire or deformed, and square or round wires were used.  Smooth round wire mesh today, I believe, is made from 65 ksi steel, and 70 ksi steel if deformed.  A number of years ago, our office did some load calculations on an old bldg built in 1919, and we used 50 ksi for square wire mesh, but I'm not sure where the design engineer got his information.  To be on the safe side, I'd be conservative with it and stay on the low side, (ie. 50 to 60 ksi).

Good luck.

Take samples and test them. You need about a one foot long section of wire for each test. Make sure it's the strand runnig parralel to the span of hte slab. I have found wire with ultimate strength as high as 80,000 psi in floors built during WWI. You should check the yield strength and ultimate strength to check toughness. your may find your slab has more capacity than you thought. You need to check placement as well. Is the fabric giving you adequate depth to develope moment capacity?