Not a common vehicle in this forum to be honest, but I did find a very nice diagram of the Lada Niva's carburetor, located here (Photos 9 and 10):
http://www.scribd.com/doc/21560551/L...stration-Album
There could be a few things going on from my limited carb experience:
1) The idle fuel adjustment screw needs to be reset.
2) The floats/needle valve are not metering fuel correctly and/or overflowing the bowl.
3) There may be a problem with the choke not disengaging after warm-up.
Does it start easily? Can you describe how it runs...if it runs? Does it run better after it has warmed up? As I understand, it runs poorly at all throttle positions with little power, but is there a position where it runs better or normal? Half way? Full throttle? Was anything else changed or repaired on the vehicle at the same time?
Hopefully, someone with more carb experience will chime in, but we are trying to help. Frustration is common, but the speed of the Internet is not instant, so please be patient. Thanks!