Gummy could be some sort of wax build up. You could try 1/2 cup White Vinegar, and 1/2 cup warm water and rub in the direction of the grain. You could also try Formbys build up remover. From the after picture it looks like you have also removed the finish.

Here is a link that might be useful: formbys remover

Great! Sorry I started this project.

Can I just spray paint these?

Jane

Chronic exposure to body oils (and attached grime) can degrade finish to the point where it is not finish any more, it's degraded goo. I've seen this a lot on dining chairs, office chairs, desk edges, etc.

A really thorough cleaning will remove the goo, but leave raw wood.

In order to put something else on it successfully, you do need to clean it all off. Otherwise, it will be soft finish over softer goo.

If Dawn & water doesn't get it there quickly enough, try Formula 409, then rinse well with water and let it dry thoroughly.

Sand lightly to remove any raised grain.

Then seal with a couple of light coats of shellac (you can get aerosol shellac "Bullseye"), that will make application on a chair go quickly. Shellac will also seal in any potential silicone oil contamination from Pledge furniture polish. If yo have this oil on there, any other finish will crater ("Fisheye") and you'll have a mess. Let the shellac dry 30-60 minutes, then top coat with finish of your choice.

Thank you. I made such a mess of these chairs by trying to clean them. It started raining and I had to stop but when I look at where I scrubbed, it looks like raw wood now. The dark, grimy parts look worse. Yikes!

I guess I can't just paint on top of the mess? There are 4 chairs, one worse than the other. Wish I could dunk them all into some chemical and just have it done with.

Thanks for the adivce. I'll buy some 409 tomorrow.

Jane

I got the impression you were going to paint them, so my advice leaned that way. If you are going with a natural finish, then you probably will need to strip them to get an even coloring. Stripping chairs is a lot of work because of all the small parts and most sides are show sides except for the bottom of the seat.

I like oil-based paint (or spray lacquer, for which you probably don't have the right equipment) for chairs.

You need to get down to clean, dry (not gummy) surface. Furniture grime is usually hand-oil based, and water-based soaps don't work well. You can't paint or stain over it because nothing will stick.

1 - mineral spirits and steel wool will take off the 'gummy" hand oils better than almost anything.

Scrub with medium/fine steel wool or a green kitchen scrubby sponge dipped in the spirits, wiping off the grime as you go.

then, wash with mild soap and water, rinse with clean water, let dry and evaluate the finish.

It might just need light sanding after that and then you can paint them.