My research specialty is in orthopedic biomechanics. For the arm motion thing, it sounds like you might want inverse kinematics or inverse dynamics. Take a look at OpenSim:
https://simtk.org/projects/opensimFor the oral appliance adjustment, I'm not sure what your output measures of interest are. If they're mechanical maybe you want to do a sensitivity analysis using FEA. Maybe look at FEBio: https://febio.org/
As for books or surveys, biomechanics is huge topic so I'm not sure what to recommend without wasting your time. If you're still defining the problem, maybe run some searches on Pubmed with the "review" and "free full text" boxes checked, and browse the results until you find which sub-sub-topic is relevant to you?
https://pubmed.ncbi.nlm.nih.gov/?term=biomechanics&filter=si...
If no one on the team knows statics, dynamics, and (if you're considering internal strain and stress) continuum mechanics, consider finding a mechanical engineer to help.