I'm having difficulty in understanding the reason of using nominative in following phrase: "Один наш постоялец видел...". I thought genitive would be the correct case, like in: "Один наших постояльцев видел..."
You are missing "из" in phrase:
Один из наших постояльцев видел...
corresponds to "one of our residents", while "один наш постоялец" is "a resident of ours". The reason why you are confused is that "один" in the latter phrase is actually not supposed to be translated as "one" - in this usage it's actually quite close to indefinite article in English (check out this question).