Mr Socks, from Commander Kitty, is a Ferret whose native language sounds like either "Dook Dook Dook" or "HRBLRUHBLRUBH" (or some variation of those letters). It's unknown if all inhabitants of Ferret speak like this, or if Mr Socks is unique in this way, though Ace at least seems to understand him.
In Kukuburi, the big white creature in this comic speaks in electronics symbols, but it doesn't seem to hinder him.
In The Order of the Stick, one of the principal characters is traumatized and finds herself unable to speak intelligibly for 150 strips. It's represented in the text by writing her dialogue in a Cryptogram, with a different translation key for every episode. All of her lines still make sense if you can read them, leading to a rather long-running Bilingual Bonus.
In PS238, there's an alien who becomes a student at the school. He's called 'Prospero' because no one has any idea what his real name is. His speech is represented as squiggles, and only Angie understands it. Word of God is that his speech is written in English using the Camouflage font, which is all squiggles. This doesn't help much; one of his speeches is actually a recipe.
The Pyros in Cuanta Vida are muffled by their masks, and it's very hard even for their teammates to actually understand what they're saying.
All major characters in Listening To 11.975 MHz are this. It isn't because they all speak foreign languages (or mathematical equations), it's because translating them gets you gibberish. The secondary characters are not much better.
Parodied in The Adventures of Dr. McNinja — Judy, the gorilla receptionist can speak very fluently in sign language, which is subtitled for the readers but which the doctor doesn't understand a word of.
Everyone and everything in Grumble is written in an unreadable language cipher. Even the sound effects.