You might want to begin by looking at what is available through some of the better online writing sites that have been developed by college writing centers for their students, such as the Purdue Online Writing Laboratory.
If you want a definitive reference book that is focused specifically on traditional grammar, rather than style, rhetoric, or general linguistics, you might invest in a copy of Oxford English Grammar. At the other extreme, you could just get one of those study guides they sell in college bookstores—the ones that are printed on a single 8.5“x11” plastic card.
If you want more than just grammar, and something more portable than OEG, there are a number of handbooks that are designed to be used in college composition classes. These typically offer some variant of Strunk & White’s style recommendations, but also go into more detail on grammar, and may include basic concepts of rhetoric and logic, advice on research methods for term papers, and a summary of citation formats. The Harbrace Handbook is one that has been around for decades and has gone through several editions.
If you want to look at language the way a linguist does, which is not necessarily the way an English teacher looks at it, I’d recommend Language Files, by the OSU Dept. of Linguistics. This is a good introduction to general linguistics.