Yes, you can use "climb over" in that sentence but then it would have a slightly different meaning. The person saying: "We've got to climb over the wall" knows they have no other choice, the only way to get over the wall, or the only convenient way, is to climb it. Whereas the person saying: "We've got to get over the wall" hasn't yet reached the conclusion that their only option is to climb it, they might use a ladder, or a jetpack. "Get over" means to get from one side of something to the other, it doesn't state how. E.g. - How did you get over the wall? - I climbed it. OR - I found a ladder. "Climb over" specifies how you got from one side of something to the other. I probably could have explained that better but I'm knackered :D I hope it helps. And the last two sentences mean the same thing.

Both ''get over'' and ''climb over'' have pretty much the same meaning! When someone ''gets over'' something, it means that the person moves or climbs over something. So, I believe that the sentence you wrote just does not sound natural, as the ''wall'' is something to be climbed up or scaled by a person, and not something where you can ''climb over or get over'', understand? For example, you could say: ''We have got to climb up the wall'' (or ''We've got to climb/scale the wall'' As for ''climb'' and ''climb up'', there's absolutely no difference between them in this context, so you can say in both ways: -I climbed the mountain. -I climbed up the mountain. If you should want to use either ''get over'' or ''climb over'' in a sentence, just remember to use the right locations, as you can see in these examples here: 1) ''Oh, there are too many sand dunes around here! We got no choice: we will have to climb over all of them!'' 2) ''I just couldn't get over that huge rock over there, so I had to go around it'' 3) ''Don't be stupid! Climbing over water is something that only exists in movies!'' I hope I have been helpful to you!