Hi! I'm more of an EDM person myself in terms of writing, but I do pull influences from Bach, Beethoven, and Stravinski occasionally. The biggest thing that I've pulled from them is the ability to convey emotions through melodies and overtones. Metal is the epitome of the darker side of music, with a lot of tritones, syncopation, trills, etc. It all has to do with layering the right voices together. Try to listen to some compositions that you enjoy, and try to pick out the different sounds going on.
I like to throw a song or composition I enjoy into some kind of DAW, like FL Studio, Logic, etc.. and try to copy each separate part. Recently, I compiled a duplicate of Joe Satriani's Always With Me, Always With You, and it helped me learn a ton about different scales, note spacing, and tonation.
Hope this helps Good luck!