Make your own miter box,very simple 2 sides and a bottom.
Lay out the 45deg. both ways and a 22.5 deg. both ways and cut them with the saw you are going to use. Make 2 boxes if you want one for each cut.
Have a 90deg. cut on one of them or use the end of the box for your 90's.
A pull saw makes an excellent miter saw, or a carpenter's handsaw, 10pt. or 12pt.
Backsaw is best if you have one.
use a coping saw to cope the inside corner, or make a coping jig for router table, like Gafboat Oliver did here on the forum.
Splice your long runs on a 45deg.
Brad nailers are great for running trim.
If the trim is going to be painted, pre prime or paint before you install it. you will be glad you did.