I'm looking for approaches to nonrenormalization theorems in supersymmetric QFT which are as much as possible mathematical, elegant and involve few heavy straightforward computations
One approach is that of Seiberg
which is also expanded upon a little bit (and explained in a slightly different way) by Weinberg
The old point of view is based on explicit supergraph computations
The disadvantage of the supergraphs approach is that it is bound to be valid only in perturbation theory. The advantage of it is that it is extremely rigorous and transparent. You said you were looking for a mathematically solid and elegant approach, so I would probably recommend this one. But the intuitive methods of Seiberg proved much more powerful because of their non-perturbative validity and simplicity.