The names of each mode go like this.
1. Ionian
2. Dorian
3. Phrygian
4. Lydian
5. Mixolydian
6. Aeolian
7. Locrian.
Therefore, in C, we have: C Ionian, D Dorian, E Phrygian, etc.
Anyway, it is a good idea to practise playing the different modes of the major scale (to start with), and listening to the way they sound. Play the second mode (Dorian) of C (by starting on D), and compare it with the sound of the D major scale. What you are doing is playing D dorian, and D Ionian. This seems to be going a little in circles, but bear with me.
A lot of Jazz songs rely heavily on modes, as solos in jazz often revolve around individual chords in a song, rather than the overall key as in most rock music.
Now, there is so much to learn about application that I don't think I can even start to scratch the surface here, lwhat I have given you is an example of an area useful to practice. By incorporating different modes, and learning how to use them, you can break out of the more common pentatonic solos that sound cool in rock, but are limiting in jazz. That could be a major reason why you still sound rocky, you aren't utilising all your notes as wel as you could be. For lessons about modes, and how to apply them to chord changes, there are several good sites that you can check. http://www.wholenote.com has good articles and dicussions about modes frequently, and http://www.zentao.com/guitar/theory has great lessons about all sorts of stuff. There is a whole world of music out there, but it takes patience. If you already know what I am telling you, I'd be happy to go further, or if there is anyting in particular you would like to know, ask me, but there is so much to cover that I can't preempt. Hope some of this helps, and doesn't confuse or patronise you.
"Dozens of people spontaneously combust each year, it's just not that widely reported".