digdug is right, evaluations do nothing but possibly hurt the feelings of the instructor who bothers to read them. you can certainly appeal grades. it's likely that if the professor is so lax about the grading he will also be lax about the appeal process, so it may well go in your favor.

you will need documentation about when you turned things in (the date you put on the assignment is meaningless, but something like an email is at least potentially verifiable.) sometimes departments will date stamp things.
you should have the original syllabus and the revised one that you should have gotten when he revised the grading system, and a clearly worked out calculation of the grades (that you think is correct). ideally you should run this by someone else (like him) before you do the appeal.

it's important not to confuse the issues. your issue is that he is marking your stuff late that is not late, and that is grading system is not well defined. the fact that he cancels class and so forth is secondary. you can mention it, but if you go into this huge litany of complaints, you're just going to look like a whiner.

the problem is that departments hear from complaining students constantly, especially undergraduates, and most of them are full of crap. I'm NOT saying you are wrong, but that's what you're up against. the more professional and organized you are about this, the better it goes for you and everyone after you.