Omnispeak is a language spoken by at least the Vorticon and the Shikadi races. Keen learned it from the Vorticons, who taught it to him after he freed them from The Grand Intellect (Mortimer McMire). It is likely that Mortimer can speak it too and that it is a commonly used space language (due to the omni- prefix).
It is very likely that the Standard Galactic Alphabet (SGA) is used to write Omnispeak. However, all signs in SGA in the game are in English, so there is no evidence of this. However, it is very probable that the Vorticon signs are actually in Omnispeak, and in the game they are in English to simplify things for the player.
The message Keen picked up at the beginning of the Keen 4 story was spoken in Omnispeak. However, here it was translated into English, and no Omnispeak words are ever heard in the game.