What are you planning to do with them? What is your skill level? The bits of veneer on the tops will need to come off.

If you want a natural finish on the base, you will need to chemically strip, do a light sanding, then stain and finish to your desire.

If you are going to paint them, you need 'clean and dull' Clean thoroughly with Dawn and water, then follow up with a rub down of mineral spirits or naphtha. When dry, scuff sand to dull the surface. I'd probably use Scotch-Brite non-woven abrasive pads in maroon and/or light gray grades. I'd then use BIN primer that will isolate any potential silicone oil contamination (from Pledge furniture polish) and provide a "barrier coat." Then paint with your paint of choice, but not latex.

The tops will need some work. If you're going to paint, you might get by with cleaning and light sanding. If not, they'll need re-veneered. A quick and dirty way to fix up the top would be to get some 1/4" or 1/8" hardwood plywood, glue it down and trim off around the edges. You'll see the intermediate layer, but these aren't really high end tables and you might get by with it.

Thank you so much, bobsmyuncle!

I am going to keep them and use them so I have to clean them up and make them serviceable. On a scale from 1 to 10, my skill level is -5 so I would have to have someone else do the work...I just need to be able to tell them what to do! I wasn't aware they could be re-veneered.

I'm sure I can handle the cleaning of the bases and, maybe after I see them all spruced up, I can figure out whether or not I want to paint them or not. Or, maybe when I see what the possibilities are for the tops, I can have a better idea of what direction to go in.

They can be re-veneered.

However, cleaning them up, sanding the tops to remove the damaged wood and painting the tops might be a more budget-friendly fix.

For the cleanup, here's my method, regardless of whether I am planning to paint, refinish or just admire the results:

1 - mild soap and warm water and a plastic dish scrubby to remove the water-soluble dirt and solidified dust. Use toothbrushes and whatever you have to for the cracks.

Rinse and dry with clean cloths.

2 - repeat the cleaning with deodorized mineral spirits to remove oily grime. Wipe it down with clean cloths. (yes, I wash a lot of rags when I'm cleaning old furniture)

3 - Now that it's clean, you can evaluate the finish ... figure out what is left, what it is and how to either remove it or fix it.

To expand on Lazygardens, see the link below. You might be able to resurrect the bases with a lot of cleaning and a bit of shellac or lacquer sprayed on (aerosol cans of either)

Here is a link that might be useful: Saving the Finish

This is really good information!! Looks like I will be curling up with a small bowl of soapy water, a big bottle of mineral spirits and a giant bucket of elbow grease. It has also been suggested that I seek out furniture restoration places to see what they recommend so I will do that as well.

Thank you both!