Any ideas on how to replicate this effect? Squished Text

That's pretty clearly a Bezier Warp applied to each letter separately.

Mylenium

You can use many of the Distortion effects applied to the text layer can generate that kind of animation. Everything from Displacement Map with an animated gradient to Reshape driven by animated masks to Mesh Warp would do the trick. I would probably start with Reshape, then maybe try Mesh Warp.