The body has different natural processes that occur throughout the day and night. Choose one of these and research the causes of the function. It is unlikely that anyone else in your class is going to write a paper on the positive characteristics of passing gas or why belching is necessary. Keep the topic tasteful and precise to ensure the teacher will accept it and appreciate the research.
New and interesting things are happening in the news all the time. A UFO sighting or meteorite shower could offer just the touch of weird you are looking for in your research paper. Check out the local tabloid papers for two-headed babies, or other strange occurrences, which might have some piece of fact to them that you could incorporate into a well-rounded research paper.
Check out the latest world records and research one of those topics. Many of the topics are a bit weird. The largest Christmas stocking or biggest speed dating event would offer a wealth of information for a research paper. Browse the current and past world records to find one that particularly catches your eye and begin researching it.
Think about the things you find fascinating or weird in your daily life and consider writing about one of those topics. Add your own weird twist to any subject to make it more interesting to the reader. If you like skateboarding, writing a research paper on that would probably not seem weird, so write a paper about the different types of horrible injuries that could occur, for example.