How can I check a used lens for internal fog or haze?

To do this professionally:

You need to have a special piece of equipment called a lens test projector. You can take it to a good camera rental house and ask them to do you a favor and check the lens. Or mail it in to get repair, $$.

To do this on the cheap and not very scientifically:

If you have a magnifying glass or good eyes a close visual inspection through the lens in high light would probably be enough to notice element problems. remember not to look at a light through your lens and go blind okay.

You could buy or print a camera test pattern and take a bunch of photos of it then zoom in and look at them. If you move the paper slightly you will see similar distortions appear at the same spots regardless of paper orientation and position.

On a personal note, i washed one of my camera lenses through a full cycle and load of clothes. I never used it again, but a few days in rice, and a large silica pack removed almost all the moisture from inside the lens. The lens tech that looked at it had to screw it back together and when she put it on the projector it was noticeable that it was damaged by washing machine.