Why does Sylvester Stallone talk so weird?

Sly has tinnitus.

Tinnitus can have many different causes, but most commonly results from otologic disorders – the same conditions that cause hearing loss. The most common cause is noise-induced hearing loss, resulting from exposure to excessive or loud noises. Ototoxic drugs can cause tinnitus either secondary to hearing loss or without hearing loss, and may increase the damage done by exposure to loud noise, even at doses that are not in themselves ototoxic.

It is the chief reason that his voice sounds so "weird".

He is one of a number of notable individuals with this condition:

https://en.wikipedia.org/wiki/Tinnitus