How to get the nuts/screws? out

Hey thanks for the great help. And, Cuda '67 for posting the picture. I am tyring to get the hang of modern tech but it has bee slow going. Family and friends say I can short out anything if I am in the same room and used to ban me from touching anything ha ha.
Anyway, great picture. I hope to give this a try this week,going through the trunk to turn them from the inside with vice grips. That interesting tool will be my last resort as this is the only care I have with this type of screw. My 68 Charger has Phillps screws. Again, I can't thank all of you enough for the help you have provided. I am within a month of painting the underside. Can you believe, with the car stitting on jack stands (no motor or tranny), and NEVER having done this before, I droped the front suspension, torsion bars, K frame and all, leaf springs and rear end in the back, so that nothing is in the engine bay or under the car and, and, I have sanded down the entire engine bay (hand sanding and some hand tools), and the entire underside? Yep. I took off the front fenders and have sanded that area as well...oh, I forgot to add, I used a heat gun and removed pounds of undercoating (that was fun) front to back. I learned how to do all of this FROM THIS FORUM, fom all of you. Thanks a million