What is the difference between let me tell you about my family and let me talk to you about my family ?Feel free to just provide example sentences.

To tell means to relate something. Like telling someone a story. Telling you about my family means I want to share some family history and details that you might find interesting.
To talk to someone about something means he/she has a topic or problem in mind and wants to tell you so you will understand and/or can discuss it. So if I said "Let me tell you about my family" it might mean something like they are very religious so be careful how you speak around them. Or they are very old-fashioned. Or they don't watch TV. Something like that.