I don't worry about cutting on the straight grain. I cut all my strips Width Of Fabric (WOF). If you want to find the straight grain sewing quilt pieces together, just tug a bit, if it doesn't stretch at all it is on the grain. I try to sew all of pieces together on grain. My Daughter never does and I am not sure anyone can tell.
I star when quilt pieces were cut like yours. I was so grateful when I learned about rotary cutters. mats and rulers. I have made probably close to 400 quilts, comforters and biscuit quilts. I could not have done that many using the old way.
Welcome to this board, lots of knowledgeable people here.