Here are my thoughts on multiclassing for you.
Cleric: I would forget about taking any cleric levels. They will just slow you down. Tell the paladin "Thanks, but no thanks!"
Barbarian: One level could be useful. You get a Fort save boost, a d12 HD, and rage once per day. Fast movement is alright, but you want heavy armor a.s.a.p. BTW, in medium armor, you add +10 to your base speed. A dwarf's base speed is 20, so your base speed is 30 in medium armor or less. The medium armor, however, lowers your speed to 20. Don't get another level. The uncanny dodge will not help you that much with your current dex.
Rogue: Three levels of rogue could be quite useful for you. Skills, sneak attack, evasion, uncanny dodge, and good reflex saves will broaden your character nicely. The disadvantages of course are lower possible hit points, 1 less BAB, and loss of bonus feats.
Fighter: Staying with fighter is a viable choice, too. Bonus feats and weapon specialization (dwarven waraxe) at 4th level is not too shabby.
Here are a couple of ideas on how to proceed:
L3 - Fighter 3 Cleave
L4 - Fighter 4 Weapon Specialization (dwarven waraxe), Str 19
L5 - Fighter 4/Barbarian 1 Rage, Fast Movement
L6 - Fighter 5/Barbarian 1 Great Cleave
L7 - Fighter 6/Barbarian 1 Improved Initiative
L8 - Fighter 7/Barbarian 1 Str 20 (+5)
L9 - Fighter 8/Barbarian 1 Improved Crit (dwarven waraxe), Power Lunge
L3 - Ftr 3 Cleave
L4 - Ftr 4 Weapon Specialization (dwarven waraxe), Dex 14
L5 - Ftr 4/Rogue 1 Sneak Attack +1d6
L6 - Ftr 4/Rogue 2 Evasion, Arterial Strike (song & silence)
L7 - Ftr 4/Rogue 3 Uncanny Dodge, Sneak Attack +2d6
L8 - Ftr 5/Rogue 3 Str 19
L9 - Ftr 6/Rogue 3 Improved Crit (dwarven waraxe), Imp. Init.