Do you need premission to make characters that pay homage to older movies?

Better safe than sorry. Copyright is a very serious issue in the arts business. Asking for permission is very necessary and will not give problems in the future should your game end up big.

It's all of a manner of context here... In short, the closer you design your monsters to a copyrighted character, the more likely you'll have to get permission (or a license agreement pounded out) to use them. If your character can be confused with an existing character, you're probably too close for legal comfort.

Please be aware that corporate copyrights last around 95 years old (personal copyrights are generally 70 years OR the life of the creator, whichever comes first), so the ORIGINAL King Kong won't hit the Public Domain until 2028 (as it was released in 1933)... Godzilla hits Public Domain in 2049... Attack of the 50 Foot Woman hits the Public Domain in 2053 for their ORIGINAL RELEASE VERSIONS (newer versions of these characters won't hit the Public Domain until much later).

LEGAL DISCLAIMER: I AM NOT A LAWYER & Information I'm providing is subject to error, but is based on best-known information available. If you're seriously concerned about this, please contact a lawyer that specializes in copyright law for legal advice.

If you make your own creatures that have some inspiration from existing characters, as long as you're not directly copying a majority of aspects, you should be OK.