I agree with LI. Don't eliminate anything but in each internship mention experience directly related to the job you are applying for even if you have to be a little creative and come up with a way to link your experience with the job you are applying for. For those without a lot of related experience give a shorter summary description of your experience, this will prevent the reader from getting overwhelmed trying to understand exactly what you really have the best experience in. In the end you want the reader to think you have the best experience in the type of work you are applying for, because it is was always on your career path to devote your career to this type of work experience and the job you are applying for (rather than just a pile of unrelated experience).
It is the same thing when you work for real and build your resume. If you start your career in a specific field because that is what you like to do you would necessarily keep on that path and have similar jobs but with more and more responsibilities and higher positions, if you go work for other companies. This is a good career path. If all of a sudden you go to work in a totally unrelated field, as a Chem E but unrelated experience, for a few years and then want to come back to the original field, resume reviewers are going to wonder why, like this guy don't really know what he wants to do or maybe if we hire him in a short while he will leave for something unrelated that he really wants to do, and also think you have such a gap that you might have fell behind in your field. You must show a that you have a definite career path and that you are always progressing in that path to stay competitive with people at your same level.