I'd either stick with barbarian or fighter. Diluting it too much more and you suffer.
Pick fighter if you want to grab some cool tricks with the feats, and barbarian if not.
If you don't continue with barbarian I recommend extra rage to boost your rounds.
If you want to, and with GM permission, you could retrain into the viking fighter archetype. That would give you full barbarian rage and the feats of a fighter.
With stats like that, why aren't you a monk or skald.
As for your question, are you asking if a third class would wise/good/viable? Probably not. Your group is missing a divine caster though it's a little late to do anything about that because multiclassed casters don't do too well.
This won't be optimal but a level in oracle will qualify you for Holy Vindicator which progresses those spells a little bit. Another level in barbarian nets you more rage rounds and the opportunity to enter Rage Prophet and with stats like yours, a rage prophet could work. I say oracle instead of cleric because you can pick up the lame curse which you slows you down but eventually makes you immune to fatigue and you'll be able to rage cycle.
A level in Bard, Skald, Sorcerer, or Eldritch Scion Magus lets you enter Dragon Disciple. Your party has a sorcerer and bard already so I'd stay away from arcane classes.
These prestige options all require ranks in knowledge skills that you probably don't have but it is possible to retrain skill ranks. Other potential third classes include a two level dip in Paladin or a level in lore oracle. The paladin dip is to get your decent charisma to saves and the oracle dip is to get charisma added to your dex for AC and saves. Both offer wand and scroll(maybe) usage.
Personally I'd try to make a rage prophet with a lore oracle but I'm known for playing weak characters. A full oracle or barbarian would do better. You should probably stick to fighter unless you're ok with lowering your effectiveness and playing a niche build.
He can't dip in paladin, barbarian and paladins doesn't have alignment compatibility.
However the rage prophet looks interesting, your party lacks divine magic and it will help with that
He can't dip in paladin, barbarian and paladins doesn't have alignment compatibility.
However the rage prophet looks interesting, your party lacks divine magic and it will help with that
Theres nothing wrong with being an ex-barbarian, he can change alignment and keep his rage but again, a third class is niche.
As for Inquisitor, I don't know enough to give good advice but I'm pretty sure heir abilities scale with level, something you can't really afford, and they don't look too tanky either.
Retrain Cleave to Quick Draw, and broaden your weapon inventory to include an Adaptable bow and a polearm. (Retrain Combat Expertise to Combat Reflexes if you really take a liking to AoO-generation with the polearm.)
As far as a third class....Warpriest seems like the best fit for both the character as well as the party's needs.
Dipping a level of cleric (I wouldn't take more than 3) loses you 1 BAB but gives you wand and scroll use which can be huge for healing and condition removal, which your party sorely lacks. If you pick Travel domain you get +10' move which is very handy for a martial. This depends on your alignment, of course.
Alternatively, dip ranger for (fewer) wands and scrolls, but more skills and no loss of BAB. Or Bloodrager for +10' more move (they stack!).