I am aware that the Men in Black comic book series is owned by Malibu Comics, which itself was bought out by Marvel. Because of this weird ownership, does the series belong in any Marvel continuity or canon? It couldn't be part of the main Earth-616 universe, as aliens are an everyday occurrence there. Does the comic belong to a specific universe, or is it in one all its own?
No, it doesn't belong in the Marvel continuity. Marvel's Earth 6716 does have their own Men in Black, but they are servants of Seth, and they are out to kill Asgardians (Thor and co.)