3L Friends who summered at firms said their career offices do sometimes take flyers on non-OCI students, especially if they have good credentials or interesting backgrounds. I have gotten a few full interviews off of the unsolicited resume drop. It also may help you if you can locate an undergrad alumnus connection at your target firm. These people tend to wax nostalgic about the good ol' days.
The most important thing is to make yourself available to employers. I was going to be in a target market for a callback, so I called a firm I had not heard from (but others had) and said I would be in town; would they like to see me? They did, and I now have a callback. Sometimes you just need to be proactive.
Looking in non-traditional, but very good legal markets might also help. Delaware is a strong corporate market, but really doesn't have any stellar local law school. Good credentials from a reputable school can get you into the market (or others like it with few regional law schools). A job is a job, and if you keep your good marks up you can either lateral after a year's experience or clerk after law school and get a second crack at the job market.
Also keep in mind that mid-sized and small firms don't know their hiring needs until the last minute. If you can't snag something through OCI, you will likely be able to beat out 1Ls for summer spots with these employers.