The primal rager prestige class (Dragon 395, p70) gives a nifty ability at 1st level called strength of the beast. It allows you to subtract a number from the duration of your rage and add the same number to the str and con bonuses granted. The number is capped at the sum of your levels in barbarian and primal rager. As an odd quirk, you don't get to count the con bonus from this ability for determining the duration of your rage.
So, a barbarian 8 / primal rager 1 / barbarian +11 could gain +26 to str and con while raging. Dealing with the -20 rounds of duration would seem to require multiple instances the extend rage feat. On the plus side, there's finally a use for extend rage. On the down side, this eats up feats (improved unarmed strike and iron will as prerequisites, and however many instances of extend rage) and forces you to stick with two specific classes, neither of which has much to offer after 1st level.
The mighty contender of Kord prestige class (Dragon 283, p46) has two cool abilities. Feat of strength, given at 1st level, lets you use the granted power of the strength domain a number of times per day equal to your “unmodified” str modifier and lets levels in the prestige class stack with cleric levels for the granted power of the strength domain. Surge of strength, given at 3rd level, makes the granted power of the strength domain last for 1+1d4 rounds. The domain focus ACF (Dragon 347, p91) for cleric doubles the benefit of a domain but costs you the other one and your spontaneous casting ability.
So, a cleric (domain focus: strength) 8 / mighty contender of Kord 3 / cleric +9 could gain a +40 enhancement bonus to strength for 1+1d4 rounds as a free action some number of times per day. On the down side, mighty contender of Kord only advances casting at even-numbered levels, so you're behind by two on casting. Another downside is that you need to stick with cleric or those few prestige classes that stack for domain granted powers. I can only think of ordained champion (which isn't compatible with Kord) and paragnostic apostle.