I have an old drill press, it has sort of oscillated, like the top of a drill bit gos in a circle, for as long as I've owned it. At one time years ago I read about knocking the Chuck off with a sledge and rotating it 180°, I did that and it helped (not perfect). Recently the Chuck fell off and I re installed it with red lock tight, but I guess I got it wrong, as it oscillates real bad. If I put the bit in a jig hole without clamping the jig down the jig moves around about a quarter inch.
I'm wondering if I could just hit it with a sledge sideways to true it? This is a big old drill press I have had for about 20 years, I paid quite a bit for it and I'm probably not going to be using it much any more, but I have a couple projects I need to finish and I'm tempted to buy a new smaller press for $100~ locally. No guarantee that'll even be true.
ETA: I hope this is ok to post this in the gun smithing forum, didn't know where else to post and I do use it almost exclusively on guns.

I'd knock the chuck off and use a dial indicator to check the arbor. It may be bent, have a gouge or burr, or loose bearings.

If the arbor runs true the problem is probably the chuck. Some nicer chucks can be rebuilt using a rebuild kit. Worn chuck jaws can cause runnout issues. Or just replace the chuck.