Undergraduate research in math, but no research paper, will this hurt me in graduate admissions?
Speaking as someone in field not too far from yours:  sure, it would help if you had done all of the stuff you've listed and written a paper about it.  But having a bunch of conference presentations under your belt (oral and posters) is still pretty impressive;  and there are many applicants to Ph.D. programs without any research experience at all.  The fact that you've done research, and that your advisor thought it was worth presenting at multiple conferences, is a pretty big item in your favor.  

Oh, and it should go without saying that this professor should be one of your recommenders (absent any major falling-out or other complicating circumstances.)