The half-giant monster entry lists Powerful Build as a Special Quality. Alternate Form explicitly lets you retain those, so yes, a druid with Powerful Build does retain that bonus, which is sizable. Powerful Build explicitly stacks with things that change your size, so if the druid used Wild Shape to turn into a Large creature, he would count as Huge for the purposes listed in Powerful Build.

See here for a list of options for obtaining Powerful Build. Note that all of them have positive Level Adjustment, which the homebrew lesser half-giant you found does not. Many DMs would balk at that. In reality, Powerful Build on its own probably doesn’t justify LA +1, but Wizards evaluated it as such. Level Adjustment is bad in general, but truly awful for spellcasters. And the half-giant race has nothing else of use or value to a druid, though use of the Primordial Giant template from Secrets of Xen’drik, at least, would make the half-giant more caster-ly (though still nothing particularly relevant to druids).

Looks like a Huge weapon works without penalty

Wield Oversize Weapon says you can treat a weapon as one size category smaller than it is. Thus, you can treat a Huge weapon as if it were Large.

Powerful Build says you can wield weapons one size category larger than yourself without penalty. Since a goliath is a Medium creature, that means a goliath may wield Large weapons without penalty.

Since Wield Oversize Weapon lets you treat the Huge weapon as Large, and Powerful Build lets you wield Large weapons without penalty, you may wield a Huge weapon without penalty.

It does appear that by preventing Wield Oversize Weapon from working with Monkey Grip, the authors were trying to prevent exactly this, which could be an argument for an intent that this shouldn’t work. But by the rules-as-written, that applies only to Monkey Grip, not Powerful Build.

Please note that a size category larger weapon tends to deal only ~1 more damage than its smaller counterpart. There are some exceptions, but it still tends to be small amounts of damage. You can often gain more damage more quickly through other uses of feats. Note also that the size of your weapon does not affect reach (well, larger weapons don’t; too-small weapons do), so you do not get extended reach this way, either.

As for gloves of enlarge weapon, those are a really poor idea. If you meant strongarm bracers, those explicitly do not stack with Powerful Build.