I encountered similar situations often during my job searches. The worst applications used these cumbersome billion-question systems where you'd need to fill out information going all the way back to high school. My general advice is to fill out everything. Departments usually put the ads together, but the online systems may well be run by HR and have to adhere to specific guidelines beyond the department or even beyond the institution itself. Some state institutions have all sorts of specific requirements mandated on a government level.
Regarding a situation where the file "slots" are inconsistent, I recommend having your cover letter, CV, and teaching statement all as one PDF file. This would be uploaded into the "teaching statement" slot in this case. Add the research statement separate. For the manuscripts, I'd add a list of publications as a document file straight from my CV and would include sample publications after that, again, as one PDF file similar to what juniorfaculty suggested.