The Viper is an FR car, so will oversteer anyway. The normal one has 500hp, which only makes things worse. The full-tune one has 1000hp - imagine the fun.
Get your Traction Control ON - at least to 1, possibly 2 given the high power. The longer gearing you have helps. Try using manual transmission and changing up a gear before you accelerate too. Increase downforce to maximum.
You'll want to stiffen up those springs from stock. Set it to 10.0/10.0 and take her for a spin. If it's still oversteering, increase the rear springs by 1.0. If it still oversteers, increase it some more, and so on.
Increase stabiliser settings - 4/4 is a good bet on most cars.
Set front toe to -0.5 - that will help the car turn in better and negate oversteer a little. Increase rear camber so it is closer to front camber - try 2.5/2.2.
If you don't have one, buy a Fully Customised Limited Slip Differential. Set it to 0/60 all round.
And if NONE of this works, get a different car and learn how to drive first, before taking a stupid, overpowered lump out on track. In most cases, the biggest Turbo/NA upgrade is unnecessary and can LOSE you time through lack of car control.