In your sample sentences, there is very little different as you use "I will try". However, I shall explain the differences if we are just focusing on the prepositional verbs.
To ask somebody to do means to request. This would be of course the most polite way of getting what you want.
To get somebody to do would mean that you are ordering them.
To make somebody do means you are ordering them as well, but implies the juse of force.
This would be the strongest way of getting what you want.
I hope this helps.