I'm relatively new as well, but I don't think you should be messing with your bridge and string settings until you check everything in your technique. Follow Fiddlerman's advice.
Also, do you have a decent violin to start with? Could be that a cheapo violin just won't make a good pizzicato sound.
I tried anchoring my plucking hand and pressing a bit harder and that seemed to help quite a bit.
Thank you all for the help. What triggered this issue was that I purchased a fingerboard guide the runs all the way up to the nut, under the strings. When I installed it the guide was flat and secure, but made a affect when played....made everything sound dull after the installation. Now I am just considering getting some fingerboard tape instead.
Then I was also practicing pizzicato and had almost the same kind of sound. But after anchoring my hand it does sound quite a bit better.
@aaarneson I have played a few songs with substantial pizz and I had some good instruction on how to make it sound fuller and less of a dull thud. I found if I pluck with more of the big fat pad of my finger, and totally avoid the tip (and nail) it seems to sound a bit richer. I also have more success if I anchor my right thumb on the corner of the fingerboard closest to the floor (or e string, if that makes sense). I think it definitely takes practice too, though. I have a teacher who made it sound so rich and full.
When I first started, I used a few different types of fingerguides and had the same issue with it affecting the sound. If it's not perfectly flat against the fingerboard (has bubbles) then it can touch the string near the nut as the gap between the string and fingerboard becomes really narrow and causes a buzzing sound or a dull sound on the string. The fingerguide was definitely helpful but I would personally try to outgrow it as quickly as possible and start relying on your ear to tell if your finger is in the right spot.
For plucking; my teacher gave me some advice that was really helpful in my sound. When you pluck, use the fleshy pad of your finger as opposed to the tip or nail. Pluck smoothly and diagonally away from you as opposed to straight across. I had also been using to much of a downward force with my right finger (pressing into the fingerboard) which was causing the strings to sound too loud and disjointed.
Hopefully that helps! Good pizzicato is tough; I still work on it everyday.