I don't usually cut on bias unless there is a curve and never have a problem with binding odd shapes. You just need to do either Eleanor Burn's way or Kaye Wood's way of binding. You come to the corner or edge (no matter the angle) and STOP 1/4 inch from the next edge..... turn your project so the right side of your 1/4 in foot is on the edge of the next edge (or side) and BACK STITCH off the project. You can either cut these threads or not (until you get use to the procedure I'd cut them). You then fold your binding away from your project so the raw edges of the binding make a straight line with your projects next edge needing binding. This creates a fold in the binding that is the correct angle for the 'turn' on your project. You then fold your binding back down onto your fabric, but keep the angle you made by folding back the binding and create another fold at the raw edge of your fabric you just sewed. The second fold in the binding should be along the edge of the project you just sewed the binding to. Don't have it hang over or short.... This is what creates a great turn on corners any angle..... This is El's way, Kaye's you sew diagonal from your stop point to the corner. I always found El's way easier...
I know it sound confusing, but check out their videos. El's is on her site at quiltinaday.com and Kaye's is on youtube.
Good luck!