I was wondering what effects Plasticity has on Leap/Climb, Phasing, and Hypersonic Speed? I think it negates LC, but what about the other two?

I don't think it affects any of them. LC, Phasing and HSS all prevent a character from having to roll to break away. Plasticity only makes it harder for a character to break away.

None, nil and nada

Plasticity only effects you when you have to roll to break away. None of those require a roll

BigSoph is correct. Plasticity pretty much gets ignored by all the auto breakaway powers. There is a feat that helps it but I can't think of what it is right now.
Plasticity will effect Giants trying to breakaway however. Giant rules are in the rulebook and the PAC overrides the rulebook.

Tarnish

Edit: Actually no I was wrong about the Feat. I was thinking of Construct which will stop auto breakaway powers, but that has nothing to do with Plasticity.