Can the electroweak/strong forces, and/or quantum mechanics be thought of as geometric? Can the electroweak and strong forces be written as geometric theories? - Why and why not?
Can quantum mechanics in general?
For example, the Kaluza-Klein theory explains the electromagnetic field as "twists" that include an extra dimension of space. (As written by Lubos Motl in a previous question). 
 A: By "geometric" I'm going to assume that you mean "having to do with the geometry of the usual 3+1 dimensions", that is, geometric in the sense that electricity and magnetism is geometric.
This is a question that was researched deeply in the 1950s especially by Coleman and Mandula after which the "Coleman-Mandula" theorem is named. As wikipedia puts it, "It states that "space-time and internal symmetries cannot be combined in any but a trivial way". Thus the internal symmetries are not related to "geometry" in the sense of our usual world.
The Coleman-Mandula theorem depends on a lot of complicated mathematics. One can imagine a bunch of ways that one could get around it. If you google Coleman-Mandula on arXiv.org, you can find papers on this subject, i.e. extensions and consequences of the Coleman-Mandula theorem, as well as papers proposing how one might get around it:
A: From Qmechanic's comment, maybe something like the noncommutative geometry approach would appeal to you. See e.g., Noncommutative standard model on Wikipedia and Alain Conne's homepage.
