As I understand it all we know about planets around other suns is information that we can gather as the planet passes in front of its sun.

First of all, does anyone know the name of this (or these) method(s) so I can research it?

And secondly, what happens if the planet is far enough off the elliptical plane that the planet never passes in front of the sun (from our point of view)? Granted this would be a highly eccentric orbit, but it could happen.

This is known as the transit method but its not the only method used to detect and gather information about extra solar planets.

 

According to wikipedia there are 7 total methods. Pulsar timing, astrometry, radial velocity, gravitational microlensing, transit method, the study of circumsteller disks, and direct observation. From what I know the most common method as of today is using radial velocity to detect the wobble of a star as the planet revolves around it.

 

If a planetary system does not exist in a similar plane as our own the transit method becomes useless.