The plural genitive forms nostrum and vestrum are used for the partitive genitive, e.g., unus nostrum, 'one of us', duo vestrum, 'two of you'.
I think nostri and vestri are generally reserved for the objective genitive, e.g., amor nostri, 'love of us (i.e., 'love which is felt for us')'.
Whether I'm right about the objective genitive or not, it certainly seems that these genitives aren't used to indicate possession, for which you use the adjectives noster and vester. Itaque, the best rule is to translate noster as 'our' and nostrum and nostri as 'of us'; vester as 'your' and vestrum and vestri as 'of you'.
It's much the same story with the adjectives meus, tuus, and suus, 'my', 'your', and 'his/her/their', versus the genitives mei, tui, and sui, 'of me', 'of you', 'of him/her/them'.