Identifying Tranny/Axle Problems

[poetic penguin]

*Brackets can be skipped for faster reading; I added it because I think the info could be linked with the problems I'm having with my car.

Ever since I've got my 05' SRT-4, I have been researching/practicing more driving techniques rather than what's under my hood because I know jack squat about working on my car. I can't even change my own oil x) Well straight to the point, gears 1, 2, and 3 feels really sticky when I accelerate. The magnitude of stickyness lessens as I move up the gears. I know this isn't really smart, but when I bring the car to red line a few times, the gears start to feel smoother. The smoothness is only temporary though; the next day it will feel like I'm dragging an anchor again. I know for sure that this is a problem, but I don't know what problem this is to explain it to the dealership.

[I've got about 21,000 miles on my car and drive it "street" hard not "track" hard. I've autocrossed once and "drag raced" about 5 times with the street racing team around here. The roads where we race are completely smooth with no sand, gravel, or any dirt (near the airport) with scouts 1-2 miles ahead and behind us. It's like a drag strip minus the chirstmas tree lights. I always launch at 3,700 rpm because any higher, the transmission would bog the car down. I launch differently too. I pull the e-brake and let in first gear with the clutch half way depressed; I don't push the clutch down, rev, and let the clutch in.]

There are some vibrations coming from the right of my car too. But the vibration was never there for the first 0~15,000 miles I've had my car. I'm sure that there are other problems with my car too; the only problem is that I don't know what to look for.

Could someone knowledgeable here please list problems and specific symptoms that could be felt during driving as a result of a transmission or axle problem?