Title says it all. Looking for good strength training for the abs but without a) a machine b) a crunch/situp
Surely other exercised work your abs - so what’s the next best option?
There are many other excellent ab exercises. I won’t link 'cause I’m posting from my phone but if you search for the exercise ‘plank’ you’ll get a very good one. You could also search for my personal favourite the ab wheel.
A good basic exercise to strengthen the abs is to perform good ol’ push-ups with your hands in a position further away from your face, aligned with the top of your head. Don’t do too many right away if you haven’t been training abs. You WILL be sore.
In that link, what is the “starting position” you are to return to after doing a “plank” for the predetermined period of time? Laying flat on your face wondering why you’re doing this?
Just touch your knees down.
Will laying on my stomach wishing I was dead be acceptable?
Free-weight squats, especially overhead squats, will work your abs better than any other exercise. They’re even better for your abs than situps.
Wouldn’t the bees on the underside object or are they trained to move out of the way? 
I remember many years ago seeing film of Muhammad Ali training. He was laid on his back with his trainer standing over him bouncing a medicine ball off his abs so hard that he could catch it on the rebound.
I should note that he may have built up to that gradually.
do you need a bar bell for these, or will dumbbells work?
Actually, the answer is all of the above. Really, the key to developing any muscle is variation. No matter how you exercise your abdominal muscles, you’ll want to change up your routine often enough that you’ll exercise accessory muscles enough to develop a strong total core instead of only a subset.
stomach isolations.
Ever seen a dancer ripple the ab muscles from bottom up, or top down? Those.
Lay on your back, watch tv or read a book and ripple. You can combine them with kegels.
It can even be done while laying there in pain with a pulled muscle in your back as it doesnt use the back muscles at all.