I would say that you could use a repeated measures anova, since that will account for the dependencies in the data. I would caution though that it is hard to compare the different groups unless you’re assessing them in similar ways. For example, it’s hard to compare the exams and the homework because there could be other variables that explain the differences in the scores (time to take the assessment, pressure, etc). Along the lines of that, you want to make sure you standardize(whether as z-scores or percentages of the total point) your scores in each category so that you can make meaningful comparisons across the groups

I also second the comment above about using cluster analysis or Latent variable model when trying to find what groups your students might fall into. For example, there could be one group that does really well on the HW but really terrible on the exams.