I'm sure this won't be a popular option, but we just did the floors in our rented 1940s home using Flecto's "Renewal" (Varathane) kit and I must say, the floors look dynamite.
Admittedly, had I been the owner of the house, I would have had the floors sanded and the refinising done in a more traditional manner, but for 200 bucks plus some incidentals like gloves (thanks Henry!) and scrubbing pads, plus a few hours labour, we got floors that made the landlady gasp and say "they look just like they did when I was a girl!"
I did go over some of the floors first with mineral spirits to remove any remaining floor wax, but there was so little remaining after the abuses of the last who knows how many years, it was almost unnecessary.
If you have spots where the wear and tear has gone down to bare wood you're not supposed to use the stuff, but we did, and it still looks really good!
Personally, I don't see why a full blown stripper would be a bad idea if you've got many years worth of finishes, cleaner buildup and grime on the floor...but that's just my $0.02