They are three completely different items. Nosotros is a subject pronoun. It's like saying "We." So, use it the same way you use yo, tú, él, ella, etc. Nosotros tenemos una casa. = We have a house. Nos is an object pronoun. An object pronoun will either directly or indirectly be the recipient of an action. We use "us" in English for this. For example: He gave us a present. = Él nos dio un regalo. He touched us. = Él nos tocó. Nuestro and Nuestra show ownership. In English, we use "our" to mean this. Nuestro is used when the word object you own is maculine. Nuestra is used when the object you own is feminine. Nuestro hijo tiene 10 años. = Our son is ten years old. Nuestra hija tiene 10 años. = Our daughter is ten years old. Nuestro and nuestra also change depending on how many is owned. When the item is only one item, you use nuestro or nuestra. When there is more than one item, you use nuestros or nuestras. So, if you have one "casa," then you use nuestra. If you have several houses, then you use "nuestras." I hope that helps explain things a bit.

Nuestra casa es grande. Our house is big. Está casa la pertenence a nosotros. This house belongs to us. Nos is a direct/indirect object pronoun and is used generally in reflexive statements. Of course, I am a gringo just learning or relearning Spanish so you will get clearer answers from a better Spanish speaking person, Just wanted to offer something until you get those..

És muy sencillo: 1. NOS: works like a pronoun and it refers to us. It could go after the subject Nosotros but it's not necessary to put the subject. Examples: A nosotros NOS gusta ir al cine. Nos vemos después. Queremos verNOS dentro de poco. Nos gustaría ir de viaje. 2. NOSOTROS: is a subject. Like"we". Example: NOSOTROS estamos en el cine. 3. NUESTRA: is a femenin possessive ("our"). It goes before the noun or after the verb. Examples: Nuestra butaca es de color rojo. Esta entrada es NUESTRA.