The former owners of my new house (built 1980) took the ceiling fan with them when they moved out. I found 1 red wire and 3 white wires hanging down loose with cap nuts on each and a bundle of 3 black wires wrapped together with 1 cap nut and tucked way up in the box. It is obvious the black wires have been unused for a long time.

The switch to this box has 1 red wire and 1 black wire.

My light fixture has 3 white wires together and 3 black wires together (it holds 3 bulbs). But the most perplexing part is that the dining room light and the wall outlets have no electricity now.

I literally cannot afford an electrician and I can find nothing like this in basic searches. What do I do with all these wires to get my light working and the electricity back in the dining room?

The 3 blacks are the hots and being used, leave thes alone as they are always hot. The Whites all need to be together along with the fixtures 3 whites, The 3 blacks on the fixture connect to the red wire, this comes from the switch, the black on the other terminal of the switch is one of the blacks tucked away in the Fixtures box.
Do Turn the Power off as the whites can provide a shock when interrupted. Good Luck.