can I run a 3/32 chain with a 1/8 cog and vice versa on a single speed freewheel?

Asking because I ride a 48x20 and just got a new 3/32 crankset.

You can run an 1/8" chain on 3/32 cogs/chainrings, but not the other way around. 1/8" = 4/32", so it would be too big for the 3/32" chain to fit on it.

You're going to have to get a 3/32" cog if you put on a 3/32" chain.

Like dsaul mentioned, a 3/32" chain won't even fit over the teeth and sit in the valleys of a 1/8" cog or chainring.

Can't run 3/32 chain on 1/8 cog/chainring. The inverse (1/8 chain on 3/32 cog and/or chainring) runs fine.

Note that "3/32 chain" means a whole range of chain widths, from 7/8-speed all the way to 12-speed; and the same can be said of "3/32 cogs" and "3/32 chainrings".

...if you decide to run a 1/8" chain, the sloppy fit on the chain wheel usually results in some unwanted noise from the drive train. It will work, but you're way better off using a 3/32 rear cog and a chain to match it all. They're available.