Haven't had any experience with Alchemist, and barely read up on it. Ditto for Cavalier, but that's because it just seems boring.
Witch I haven't read up on, but did play in a game with one for levels 5-8, and I have to say....he really, really sucked. Kept spending standard actions to give people -2 to hit or AC (IF they failed a save!) for one round. Oh, he had the option of blowing actions in later rounds to maintain the pitiful effects. Meanwhile, the rest of us were actually killing people. In like 1-3 hits, making the cruddy debuffs seem even more pointless. Maybe it's just because our DM loved huge groups of enemies and almost never a single strong monster, but witch seemed really bad.
Inquisitor really intrigued me at first, but upon extensive reading, I came to realize that it can't actually function. I'm going to talk about an archer inquisitor, which the game seems to heavily endorse (long bow proficiency but otherwise simple weapons? and what's with lack of short bow?). If you do melee, you could've just been a cleric or druid and had level 9 casting with basically no loss in combat ability. So...archery
The class mostly fails due to lack of feats. Archery needs 3 feats (well, Precise and Rapid Shot, Point Blank's just kinda forced on you) to justify focusing on it. Until you have all 3, you're not much better off with a bow than just some guy focused on melee who picks one up for kicks. A Inquisitor can't have all 3 until level 5, 3 if human. Furthermore, in Pathfinder there's a really broken feat called Step Up, that any melee character that can meet it's rigorous +1 BAB mandate is well off to take. Spellcasters have defensive casting, archers have no defense at all. Therefore, without the feat patch known as Point Blank Master from APG, using archery as your primary attack method is a suicide pact. The main archer classes (Fighter, Ranger, Zen Archer Monk) all got a pathway to freedom, but...not the Inquisitor. Even if he could take it, a non-human wouldn't have room to do so until level 7, compared to Fighter (5), Ranger (6), and Zen Archer (3). And that's if you not only give them access to the feat, but also let them ignore the feat pre-reqs. If they need the feat pre-reqs, that's another 4 levels before you can be competent after the first round when the enemy trots the 30-60 ft typical encounter starting distance to melee you. The feat issue is actually beyond frustrating, venturing into insulting, because Inquisitors DO have class bonus feats. They just happen ot be worthless. Yup, you get them at a rate second only to the fighter, but they can only be teamwork feats. Guess how many teamwork feats benefit archery. Did you guess zero? You win! Furthermore, the spell list, which looks pretty bad overall, lacks much of anything that boosts archery. And that's counting generic small benefits, like the Bless spell. If it were sorc/wiz 2/3 progression casting, you could pick up much more useful spells to synergize with the bow, and qualify for arcane archer. Oh well.
I really like archery and I was very interested in Inquisitor at first, so sorry for the wordy review, but it was just a huge letdown.
Oracle on the other hand looks very cool. I haven't played one or seen one in play yet, but I think it's the only APG class I really want to try. I didn't like the curse rules at first, as even after 10-15 levels when the benefits are supposed to outweigh the negatives, most of the time I'd still at that point rather be without the curse at all because the initial bad stuff is still so annoying. But if you stick to the least irritating ones, you can safely ignore the curse mostly. And Haunted is very flavorful, even if it could present a pain in the ass at times, I wouldn't mind playing that.
Summoner...my friend's playing one in one of my current games, it seems to do alright. He basically just plays the Eidolon like its his PC and has the summoner just fill the battlefield with pokemon-themed allies, seems fairly balanced. I'm just not that interested in summoning.