当邀请留学生住家时，可以采用以下几种表达方式：

正式邀请

Dear Mrs./Mr./Ms. [last name],

I am writing to express my interest in having you as my host family during my studies abroad. I am excited about the opportunity to learn from and experience your culture.

I would be grateful if you could provide me with more information about your household and living conditions.

Thank you for considering my request. I look forward to the possibility of meeting you soon.

Best regards,

[Your Name]

友好邀请

Hi, I'm excited to learn that you will be my host family.

My name is [Your Name], and I am [your major/field of study] student. I am coming to [country/city] for [duration of study].

I am looking forward to experiencing your culture and lifestyle. Could you please share more about your family and what I can expect in terms of accommodation and daily life？

Thank you so much for having me! I am eager to meet you and start this new chapter of my life.

Best,

[Your Name]

简洁邀请

Dear [Host's Name],

I am [Your Name], a student from [country/city] studying [subject]. I am writing to ask if you would be interested in having me as a guest in your home.

I am very grateful for the opportunity to stay with you and look forward to hearing from you soon.

Thank you,

[Your Name]

无论选择哪种方式，都要确保表达出对住家的尊重和感激之情，同时也要清晰地传达自己的需求和期望。这样可以帮助你与住家建立良好的关系，使留学生活更加顺利和愉快。