(to) get up- levantar-se, subir.

attention to following minimal detail; if an interjection, change the meaning/sense.

get up! - levante-se!

(to) wake - v.t.    despertar, acordar (also with up)- animar, ativar, avivar, estimular, excitar (generally with up), perturbar, provocar , reviver, ressucitar, , perturbar o silêncio (de uma cidade etc.)

v.i.   despertar, acordar (also with up), estar desperto, alerta ou vigilante, animar-se, pôr-se em atividade, prestar atenção (generally with up), ressucitar, reviver.

(to) stand up-       levantar-se, ficar de pé, ag­üentar,durar, ser satisfatório.

= = = = = = ==  = = = = = == = =

In a jiffy,and in a basic level I would say that:

wake up: is to rouse from sleep, awaken. (the first thing we do in early day).

to get up: to raise to our feet, to rise as from bed. (next thing we do in early day)

to stand up: became erect/upright , the action of standing. (from then onwards we can

   do plenty of things, like brush the teeth, wash and so on.)

I hope this helps.