Will this fit my oversized aftermarket shift knob?

If your knob diameter is under 2.2 inches, it'll work. Measure across the widest point of your shifter. If you're over that spec, the fit will be loose.

Does this slide on and off easily, or does it stay put?

It's a slip-on sleeve—slides on without fasteners. It'll stay in place through normal shifting, but it's not glued down. If you want it locked permanently, you can use light adhesive on the inside, though it's not required.

Can I throw this in the wash?

Hand wash in cold water is your safest bet to keep the knit intact. Machine washing risks shrinkage or pilling. Air dry completely before putting it back on your shifter.