I've seen some movie trailers where the text just pops on the screen. Sometimes it pops on very quickly with a (bam) audio effect and then another text title or word pops on next.
Another nice effect is the screen shake.
Can these types of effects be done in Sony Movie Studio? If so, how?
Not sure what exactly you mean by your text pop description, but yes, those kinds of effects can be done (text pops & shakes), mostly just by using pan/crop. There might be a video FX for shake, but I can't remember off hand and don't have VMS in front of me.
For a simple text appearance with an audio effect, it's even easier - just put the text event on the timeline, and an audio event that lines up with the left edge of the text. Viola - sudden text with a sound effect.
I am mainly trying to figure out how to get the text titles to show up and hit the screen hard and fast like in the video above. Can this be done in Vegas?
For the text "pop" you should be able to get similar results using pan/crop and keyframes on text tracks. It will take some experimentation if you've not done it, but it is quite doable.
For the screen shake, again, you could use pan/crop to do this. Again, experimentation would do it.
You'll likely find it is a lot of work to get an effect like that shown in your link, with lots of keyframes, but it will work...