My players currently have an Astromech droid, a medical droid and a couple of scavenged Droidekas. What sort of things have you done to personalise your players' droids? Are there any rules in various supplements that cover this sort of thing?

I'm not thinking of much - just adding extra tools to the Astromech, giving other players a black die when interacting with it because it's been hanging out with one character for too long, that sort of thing.

Also, is there any sort of reduced "NPC sheet" that we can use to keep track of their stats and damage and whatnot during play?

No need for a seperate NPC sheet; if it is acting alongside the party enough, just give one player the responsibility to track its stats (on a standard character sheet) and just treat it as a PC upgraded and handled the same way, with a mechanics check to install new tools and the like on it.

While it has nothing of what you're after specifically the technician sourcebook (Special Modifications) is probably going to be a lot of help.

Special Modifications has a chart of good and bad traits a custom built Droid may have. If the book is in the group perhaps look over that list for inspiration.

I don't know about any mechanical perks to suggest, but I always think of little quirks to give them, to add personality.

I had an idea for an astromech droid for a PC group, and he was stationed on their super secret hidden rebel base, in the middle of a nowhere solar system, on an asteroid. The astromech's job, was to keep watch on the facility while the party was away, a steward of their rebel base of sorts.

Well, he would get bored, and their asteroid was small enough to not have much gravity naturally (it had artificial gravity on the inside), so he would go out on the surface, use his little thrusters to take flight, and put himself into a low orbit of the asteroid, and just stargaze. He'd pop out his sensors and just float there, soaking up all the astronomical data, making little R2 cooing noises of delight. I always planned to have the PC's first learn of this quirk, by returning to the base, and just finding him floating out there, and see how they react. Considering the mindset of most players, I would assume they thought someone had attacked the base, and it was a dead droid floating in space. Only then would I have the droid happily chirp a greeting at them, and explain he was just chilling out man. In my head, I gave him the personality of The Dude from Big Lebowski. He was just sort of...chill man, he was totally grooving on all this SPACE man. "What's that? The base? Oh sure man, it's totally cool, go on in, the larder's stocked. " And then goes back to just floating there.

I also had an idea, for the same base really, of a construction bot, whose job it was to actually hollow out the asteroid, and construct the rooms, using universal construction material and durasteel. That droid, would have some very odd quirks, in particular, a penchant for weird music from some alien planet, citing the acoustics within the asteroids he dug in, made the music exemplary. So he would seal himself in, put some atmosphere in the cavity, and then rock out while he was digging. He was also designed to be short and stumpy, basically the droid equivalent of a dwarf.

I've probably got a few other concepts in mind, but those are the only ones I can recall currently.

As far as quirks go, the droidekas are a little scared of the R2 unit, and the R2 unit is more skilled in interfacing with Clone Wars-era technology than "modern" stuff.

The droidekas may also have ... self-restraint issues ... when facing squads of soldiers in white laminate armour. I'll save that for the most inopportune time to reveal, I think.