In this case it can only mean change, the "move" meaning is to change your place of residence AND it is a reflexive verb, therefore it requires an object pronoun. "Nós precisamos nos mudar" means "We need to change our place of residence"
I think Coayuco might be overcomplicating things. Isn't this just the difference between a verb and a noun? When we say 'We need change', 'change' is a noun (we're basically saying 'We need (a) change'), but that won't work, because 'mudar' is a verb.. This is a guess, but I think it would be:
'We need change' = 'Nós precisamos de uma mudança' 'We need to change' = 'Nós precisame mudar'
Which, I suppose, is more logical than the English.
Your are right, it is a verb, noun difference. Excellent explanation btw. Also you misspelled "precisamos", you wrote "precisame"
This has a different meaning. "We need to change" acknowledges that "we" need to do something to accomplish the change. When we say "we need change", the change could come from outside, e.g. a new boss, an increase in pay, a new president, etc.
Can this be used in the context of changing clothes as well as in the 'deep' way? ;)
"Mudar de roupa" It's very informal, you may hear it but we prefer to say "trocar de roupa"
Not exactly, mudar-se means to change place of residence, it is a derived verb, and it is reflexive, they are different verbs... Even if they seem the same, they are not