Formal:
* 停留 (tíng liú): This is the most general and formal way to say "stay." It means "to stay, to remain, to sojourn."
* 居住 (jū zhù): This means "to live, to reside," and is used when talking about staying somewhere permanently or for a long period.
* 逗留 (dòu liú): This means "to linger, to delay," and implies a shorter stay than "停留."
Informal:
* 待 (dài): This is a simple and informal way to say "stay," meaning "to wait, to stay."
* 留 (liú): This is another informal way to say "stay," meaning "to stay, to remain."
Other:
* 待着 (dài zhe): This means "to stay, to remain," and is a more colloquial and informal way to say "stay."
* 待会儿 (dài huǐ er): This means "to wait a moment, to stay a while," and is used for a short stay.
Here are some examples:
* 请你在这里停留一下。(Qǐng nǐ zài zhè li tíng liú yī xià.) Please stay here for a while.
* 我在北京居住多年。(Wǒ zài Běijīng jū zhù duō nián.) I have been living in Beijing for many years.
* 我不想逗留太久。(Wǒ bù xiǎng dòu liú tài jiǔ.) I don't want to stay too long.
* 请你待在这里。(Qǐng nǐ dài zài zhè li.) Please stay here.
* 请你留下来。(Qǐng nǐ liú xià lái.) Please stay.
The best way to choose the right word is to consider the context and the level of formality you want to convey.