The Folland book mentioned here is quite good. One of the most straight-forward physics references might be Pierre Ramond's "Field Theory: A Modern Primer", but it's still a long ways from mathematical rigor. Some comments about the other books and topics discussed here:

Weinberg's books are very good in their own way, but not really appropriate for mathematicians. The first one develops QFT not so much in terms of fundamental objects, but as a phenomenological framework forced upon us by principles such as special relativity and locality. The second one does gauge theory without using geometry, or coordinate-invariant notation, which is not a great idea for mathematicians. The third one is just about SUSY, concentrating on the parts of the subject not of much mathematical interest (the IAS volumes do the opposite).

About the IAS volumes, one should keep in mind that the main point of that exercise was to try to explain to mathematicians Seiberg-Witten theory as understood by physicists in terms of N=2 supersymmetric QFT. This has nothing to do with the Standard Model, and from what I remember the Standard Model doesn't appear in those volumes. They do contain a truly spectacularly good set of lectures by Witten on QFT (but not written up by him...), aimed at getting to the Seiberg-Witten story. This involves some heavy-duty use of non-perturbative supersymmetric quantum field theory, of the sort that is of mathematical interest in building TQFTs.

Besides not explaining the Standard Model, I don't think the IAS lectures really explain the use of supersymmetry to extend the Standard Model (the MSSM "minimal supersymmetric standard model"). This is a subject that has always been heavily advertised without much explanation of its significant problems, one of which is an extra 120 or so parameters. Initial results from the LHC rule out nearly half the most popular region in parameter space, chosen for simplicity and assuming that supersymmetry can be used to solve certain problems (dark matter particle, anomaly in measurement of muon magnetic moment). This still leaves the other half, as well as a lot of other less popular regions of parameter space. Over the next year or two I believe we'll see increasingly large regions of parameter space ruled out, but there is no way the LHC can rule out all of it. All it can do is change somewhat how physicists evaluate the likelihood of nature being described by conventional supersymmetric extensions of the Standard Model, a process which has started and will continue.