"There are many strange people in our company."
Translation:В нашей компании много странных людей.
наш is the masculine nominative singular ending.
компания is feminine so the possessive takes a feminine form.
в triggers the prepositional case so the possessive must be prepositional too.
That gives us нашей. Note that for feminine words, adjectives and other determiners usually have the same form in the dative, genitive and prepositional cases, so that's a bit less to learn.