Ifyou have to move them now I'd get some biggish pots and cut the plants back before trying to move them, then dig a biggest rootball you can manage,
I think I'd water well and cut back a few days before the move, it willbe a stressful time for the plants so try to put the pots in a shady spot for the rest of the summer, don't let them dry out

not sure about the perennial sweet pea, but probably the same advice.....

Perennial sweet pea has roots that go down to Australia - I've tried moving these before, but they always regrow where they were originally, so that might just have to be sacrificed,though you can try if you want.

Wrong time to move mature plants and a photo of the one that climbs that you have no name for would be useful.

Pam's suggestion is worth a try, but be prepared for them all to not make it - you'll need pretty large pots, the largest you can find really, unless you're able to replant straight away in a pre prepared area (by that I mean thoroughly dug over so the soil is loose - the roots on plants when you dig them up are suprisingly large, so digging the right shaped hole that's also deep enough to accommodate them is much easier if the soil has already been dug).