The best I could come up with:
Race: Dwarf
Unstoppable and Stoic Negotiator racials (toughness as bonus feat, +1 fort, +2 diplomacy)
Traits: Clever Wordplay (Int to diplomacy) and wisdom of the flesh (wis for stealth)
Stats: Str (16) Dex (12) Con (16) Int (15) Wis (12) Cha (5)
Lvl 1: Armorek Hulk Barbarian and power attack
Lvls 2+: Empiricist Investigator
The strangeness...
(1) Full Plate. Usually bad for rogues. But...Wis for Stealth, Int for Perception and disable device. Trapfinding as class skill. 0 armor check penalty for any thieving skills. You now have a party scout and trap finder who wears full plate.
(2) Combat
- Str16 base with great sword
- Str18 with Enlarge Person (10ft reach and 3d6 greatswords)
- Str22 with rage (5 rounds per day, also Con20)
- Str26 with mutagen (at lvl3, also negates some of the AC loss)
- Str30 with Bull's Strength (once he gets Lvl 2 extracts)
For a great weapon build, that's a pretty high strength at a low level. With a simple +2 belt and +2 Str/+1 ain't by Lvl 12, he easily goes up to Str34. Put in power attack and furious focus, and he can bring some hurt (after 2 self buffs, of course...)
(3) Defense
At Lvl 1: 18 hp
At Lvl 2: 27 hp
+10 HP a level thereafter...on par with most barbarians
+2 HP per level when raging
AC20 at first level. -2 from enlarge person, -2 from raging, +2 from mutagen. So 18AC base at lvl3. That's...not horrible.
At Lvl 3 take furious focus. At Lvl 5 take extra traits (Magickal knack makes up for lost caster level and fighter of the society gives +1 trait AC). From there feats such as extra rage, dodge, and ironhide all help.
When he needs to tank, drink a potion of shield instead of enlarge person. Trade the +1d6 damage and +2 str for +4 shield AC. With mutagen and rage, that's 24AC. Much better for holding the line.
(4) Out of combat
- Good thief skills
- Basic Knowledge skills
- Great diplomacy (+8 at Lvl 1)
(5) Issues
- Loses 2 skill points from single class investigator
- Slower investigator progression
- Loses tons of HP, rage and powers from single class barbarian
------
And thus you have a polite, charming, dapper dwarf with a monocule. He is helpful, knowledgeable, and useful for the party. But when the enemy comes into sight, his monocule falls off, he drinks a potion or two...and he goes into a mindless killing spree.
Basically, this guy:
http://www.nuklearpower.com/2004/07/10/episode-440-berserkers-want-what-we- all-want-civilization/
I strongly doubt the trait will suddenly make Stealth not a "dex-based" skill. The trait allows you to use your modifier; However, the text in the PRD for armor check penalty still refers to "Dex-based skill checks". Unfortunately, with full plate armor, you are not stealthy. Likewise for Disable Device.
The enlarging, mutagen, shield, bull's strength, etc are all going to cost you some actions. But otherwise, fine.
Seems legit for all but the skills. I'm sure someone else can help you out if you've somehow stumbled on the math. You'd better hope his perception is good enough not to be caught off guard... Else, you're dealing with a character that works best with major buffs Before combat, and is only okay at best when caught off guard (especially if caught out of your armor).
EDIT: I stand corrected by the post below.
http://paizo.com/threads/rzs2sen0?Wisdom-in-the-Flesh-and-ACP
According to this thread, it has been FAQ'd that armor check won't apply.
"Alternate Ability Score-Based Checks: If I change the key ability score of a skill (or other check), for example, if I change Knowledge from Intelligence to Charisma, is it no-longer an Intelligence-based check? Is it now a Charisma-based check?
Generally yes—at the time of rolling a check, if you substitute the ability score, the check is now based on the new ability score. In the example, at the time of rolling, Knowledge would now be a Charisma-based skill and not an Intelligence-based skill for you, which would affect things like feats, spells, or items that grant bonuses on checks based on their key ability score (like circlet of persuasion). However, if you are adding a second ability modifier to a check, this is not the case. For instance, when adding both Wisdom and Dexterity on initiative checks, initiative is still a Dexterity check, not a Wisdom check. Also, this changes the check only at the time of rolling, so this does not change static class features or options made during character building such as your class’s class skills. Classes that receive “all Intelligence-based skills” as class skills, for instance, are the victim of sloppy writing, and furthermore sometimes effects might muddy the water by only changing the ability dependency sometimes and not others, which is why you check the new dependency only for a specific given roll."
And aye, the biggest weakness is action economy. 2 standard actions to buff up really hurts. And being caught out of armor would be bad...though that's bad for any non-Dex based martial class.
Still...so long as that faq is correct, I find the idea of a full plated, giant sword wielding, dwarven scout/thief to be amusing. And something that is, as the title suggests, an odd quirck of muliclassing
You can't combine a belt with Bull's Strength, as they're both enhancement.
The feat Extra Rage solves the problem of not getting enough rounds/day quite easily, since taking it once is worth +6/day.
A really strong alternative option for a Barbarian dip is the Savage Technologist. Unlike normal Rage, you gain +4 to STR and DEX and don't lose AC while raging (though you don't gain CON). You can take Heavy Armor anyways, but regardless you've got 4 more AC than normal.
One interesting option for the character you're looking at would be to use Savage Technologist Rage to dual-wield weapons. You only need 13 base DEX to use all the important TWF skills when you've got a +4 bump from Rage, and applying the bonus from Studied Combat to two weapons stacks up fast. Wielding two Dwarven Waraxes (with Effortless Lace) would be extremely punishing when adding 1/2 your level in damage and all that strength to two d10 weapons, though feats might be really tight on a Dwarf. Going Psychic Investigator is a pretty flavorful way to avoid any casting issues while wielding two weapons, and grants interesting stuff like using 2-round Mental Barrier spells.
Edit: Just noticed that Savage Technologist has light armor; on the up-side, taking Armor Expert and using mithral medium combined with bonus DEX and no DEX penalty is still huge armor.
I like it! The savage technologist fits the empiricist as well. Certainly a big hit to AC, but as you point out it can be overcome. Also keeping fast movement is useful...