I took a Multivariable Calculus course during senior year, and although my teacher covered everything that would be in a college level Calc III course, I feel like there’s a decent amount I didn’t completely understand / understood, but quickly forgot (For example a lot of the Green / Stokes / Divergence theorem I didn’t really understand.) In my school, I can probably waive the class without getting credit and just move on to Differential Equations or I could just retake Calc III. Is Calc III material really important for future engineering classes? What do you recommend I do?
You will be using some of the material from Calculus III, but I don’t think that it’ll merit another go at the class. The material is also very easy to pick back up when you need it.
Calculus III isn’t as important as differential equations… (I’m an Electrical Engineer 
)
You can try the old exams from your college’s calculus 3 course to see how well you know the material. For example, here are some: https://wumath.wustl.edu/exams/old-exams/math233 .