These cards are a little unusual in that they don’t really fall into any specific category. They provide support in different situations.
What the Babidi card does is unclear, but it presumably reverts any stat changes made by the enemy. When an opponent uses Gather Power, you can use Yakonto get him out of the ‘powered-up’ state.
Caps.Fridge refills 5 CC, but also costs 1, so really it gives you 4 CC. Very useful, especially in the Defense Phase, because you can never have too much CC.
Sunglasses makes Taiyoken (Solar Flare) fail. You use it before an enemy uses Taiyoken to block melee damage and then the latter will fail. – Proven by Mochi
Heart Medicine is most likely used to cancel out the effects of the Heart Virus card and is very specific if it is indeed the case.