Is it permissible to postpone giving out a vow (nazr) designated for the poor and needy from money earned through extra work in order to pay off debts and cover the costs of furnishing the apartment one will live in, given that the questioner currently resides in a highly-rented apartment?

Undertaking a vow (nadhr) is disliked (makrooh), but fulfilling it is obligatory if it is an act of obedience to Allah. If fulfilling the vow conflicts with paying off human debts, then paying off the debts takes precedence and is obligatory, because the rights of human beings are based on strictness (mushahah), unlike the rights of Allah Almighty, which are based on leniency (musamahah).