Not all decays are weak-based, though, and not all weak phenomina are directly related to radioactivity. That's just the only thing a layman has heard of where it's relevant.

The strong force only holds atoms together through a sort of trickle-down force, too, but that one feels like splitting hairs.

Well, the article currently lists them as: gravity, electromagnetism, the strong force and the weak force.

If you're not familiar, you wouldn't be able to guess that the last two are nuclear forces and in the context of a new force, that list is rather confusing.

No, there's two others, then the nuclear forces