How can I tailor my faculty application to maximize my chances at a liberal arts college? I graduated in 2007 with a mathematics degree and have since had multiple postdocs at R1 universities. While I have definitely enjoyed my experiences as a researcher, I am very interested in pursuing a career teaching at a small liberal arts institution.

So, my question is how to present my research-heavy resume in a way that is palatable to a college which may be wary of my credentials? Is it advisable to drop "invited talks/conferences" from my CV? Do I select only my favorite publications to include?

Also, I understand that it is inappropriate to give an overly detailed research statement. However, as a representation theorist, I think it is to my advantage that my research draws on a lot of different fields. Is it better to explain the broader relevance of my research, or do I ignore that in favor of what I can teach undergraduates to program on a computer? Does it make sense to write separate statements?
I wouldn't drop anything from your CV.  I might shift things around so that the "List of Courses Taught" (or that you could teach) is on page 1 or 2. Teachings awards and anything similar also up front.

The cover letter is key. Your research accomplishments should be one paragraph while discussion of your love of math, the fantastic students you interacted with at one of your postdocs, the courses you would like to teach at X, and your teaching style should be at least 2-3 paragraphs.  One thing that I did when I was applying to SLACs was to have a list of my courses in my cover letter followed by a very small print (all course syllabi listed here are available on my website: www.example.com). 

And of course you should also include a separate teaching statement if they require one -- or even hint of wanting one.