Old Home - Trying to Figure out Living Room Switches
You have a dangerous situation.

While it may not be knob and tube (an old standard that often poses serious risk), you have cloth covered wiring that is obviously deteriorating, posing a risk of short circuits and fire. For example, in the upper picture, the switch on the right has exposed wire that is a shock and fire hazard.

We could try to diagnose the switching issues (e.g., there are no three way switches illustrated), but you have a more basic problem.  This is probably the time to call in a professional to discuss replacing some of this very risky stuff.