You're not getting "attacked by spirits" because of your angel and demon heritage. You might feel yourself to have much in common with both of these spirits, but frankly, both spirits define the broad spectrum of human emotion, and it is not difficult to feel a kinship with them. Fully 75%, at least, of the "otherkin" who claim such, claim to be descended somehow from angels and/or demons.
Regardless of what you believe though, you're getting attacked because you go out lit up like a torch. You present yourself as an aggressive entity, and so spirits respond to you as such. You expect trouble, so you find it. Learn to control this and you find dealing with such things to be a much more serene matter.
As far as the description of your attacks on the spirits, I assure you that these methods, while effective in disrupting their presence for a time, rarely cause permanent harm in any way, shape or form, and I would not suggest you seek out more formidable entities.
What you are referring to is not necessarily a specific form of magic. Theses essentially amount to aggressive acts of will and energy manipulation. What I find curious about it, is that you specifically speak of avoiding dark magic and curses, and yet only speak of practicing "magic" intended for combative purposes - which in itself can be construed as dark.