The Character in question is a Large half-Minotaur Goliath who is using monkey grip.
Normally a Large Goliath could wield a Huge weapon with no penalty. Monkey Grip allows you to wield a weapon 1 size larger at a -2 penalty without changing the effort it takes to wield. So, would these effects stack and allow me to wield a Gargantuan 1-handed Weapon?
No, they do not stack.
The reason they don't is that both the racial trait and the feat reference your normal size category.
Powerful Build:
A Goliath can use weapons designed for a creature one size larger without penalty
Monkey Grip:
You can use melee weapons one size category larger than you are
In the case of a Goliath with Monkey Grip, both would be referencing the Goliath's actual size, which is Medium.
It seems to me that the qualitative nature of the respective descriptions should allow for powerful build (Races of Stone 56) and Monkey Grip (Complete Warrior 103) to stack at the DM's discretion.
Powerful build refers to the nature in which a creature is physically constructed: similar to a dwarf's stability trait (Player's Handbook 15)— that is, it appears equivalent to a racial bonus. Monkey Grip represents innumerable hours of training and exercise to increase one's natural capabilities—while obviously a feat, it can be considered something developed rather than innate.
I recognize that allowing for Monkey Grip and Powerful Build to stack is in no way necessitated by the respective descriptions. However, I believe that they are not necessarily mutually exclusive.
First, there are many qualities to a weapon that experience a simple numeric change as the weapon's size category increases (Player's Handbook 114). How is stacking a character's ability to manage these numeric changes any different from a character's ability to manage purely numeric changes due to multiple increases to a weapon's range, or multiple increases to critical ranges and modifiers. Both increases stack unless specifically mentioned.
Second, on the note of specificity, the description of the strongarm bracers (Magic Item Compendium 139) says
When wearing strongarm bracers, you can wield weapons as if you were one size category larger than normal. (You don’t take any penalty when using weapons as normal for your size.) For example, a human wearing these bracers could wield Large or Medium weapons without penalty. The effect of these bracers doesn’t stack with the powerful build trait (such as that possessed by the half-giant and goliath races).
This description specifically prohibits the ability from stacking with powerful build. This demonstrates a need for specific prohibition in relation to what kinds of abilities stack for wielding larger sized weapons. Moreover, the strongarm bracers do not specifically prohibit stacking with Monkey Grip, allowing for a Medium creature that has the Monkey Grip feat and wearing the strongarm brazers to wield huge size weapons as if they were Medium weapons at a -2 penalty. There only reason the stongarm bracers should stack with Monkey Grip but not Powerful Build is that the feat and the trait represent different kinds of benefits, and the benefit of the strongarm bracers is too similar to the powerful build trait for them to stack.
It depends on the exact wording of the Goliath's Powerful Build, which I believe states that they count as Large whenever it would benefit them. Since counting as Large for the purposes of Monkey Grip benefits you, they would stack.
The benefits of this racial trait stack with the effects of powers, abilities, and spells that change the subject’s size category.
