只需要简单说一句 “ 谢谢你们的盛情款待！” 就好啦！

If you want to express your gratitude orally, simply saying “谢谢” is fine. But since you mentioned that you want to write it down as a letter, you can use sentences like “叨扰了，承蒙款待，感激不尽”. Chinese people always like four character phrases.

说的越客气越让人觉得假！ 具体情况不太清楚，不太好说，可能可以直接说：在你家打扰了许多天，非常感谢！等等之类，根据上下文，直接说声“谢谢！”就很好！

I figure what you wanna say is: 谢谢你让我住在你家. The answer from Jiyuan is great, but I take it it's not suitable for you to write a sentence like this, because it's too formal. I will write 承蒙**感激不尽 or 感激涕零to those people who help me a lot but just have a common relationship with me. All the best.

谢谢你们让我住在你们家is grammarly correct but in a letter we usually say 承蒙款待，感激不尽