Is there any way to assign effects to only engage on certain clips?  I know you can automate off and on, my question is more, for instance assigning distortion to a specific clip and then only assign a flanger on the next clip.  Is this done through off and on automation?

Each clip has a FX rack. Keep in mind effect tails stop at the end of the clip.

I put the effect I need for a given clip or part of a sound on the whole track, then automate the effect's mix / level for that specific clip.  I would like, instead, to be able to send a clip through it's own bus, where I would have the effect. Having the effect tails stop at the end end of the clip makes it kind useless for me most of the time :)
 
Sometimes, I will set up a buss with the primary needed effects, then make two tracks of the main signal sent to that buss, with one track containing just the extra effect needed.  
 
You could also set up an effect send and automate the send level...
 
Any method seems like the same amount of effort.  For me it is an arbitrary "sense" of how it gets organized.

Like Scook said, just right click a clip and add an effect. You may want to extend the clip length if it's a delay or reverb. Also, the effect will always draw cpu power just like if it was on a track. I think VST3 handles this a bit better as a rule.

Because of the FX tail stopping, this can be an issue with specific phrases/words if they have other data immediately following when using clip FX. Because of that I often a split and shift-drag (maintain timing) to an adjacent track and use track FX on that track. Especially if a clip FX will be used more than once, the same method will save time by only requiring a single FX instance for insertion/adjustment.