1. mum's the word This is usually used in British English, I think. As an American, I get strange looks whenever I use this phrase, though most people do understand it. 2. my lips are sealed It's a fairly common phrase. 3. keep it under wraps This is a fairly common phrase too. 4. a little dickie bird has told me I've never heard anyone say this exact phrase before. However, people do say, "A little bird told me." 5. keep it to yourself Definitely a common phrase. 6. to let the cat out of the bag We usually would say, "Don't let the cat out of the bag," but yes, people do use this fairly commonly.

These are my impressions: 1. Mum's the word This strikes me as old-fashioned. It reminds me of public information posters from the Second World War. People might still use it in a jokey fashion, especially if it involves a pun around the idea of mum/mother. 2. My lips are sealed. Yes, this is used. 3. Keep it under wraps. This too, but I'd say it's less common. 4. A little dickie bird has told me. Old-fashioned and a bit cliched. The kind of thing a TV presenter might say, in a slightly artificial manner, in order to introduce a new topic with the help of a guest or co-presenter. 5. Keep it to yourself. Yes, this is common. It's normal English and it simply means 'Don't tell anyone about it.'. 6. To let the cat out of the bag. Yes, this is sometimes used. 'Spill the beans' is a similar idiom. Note that all idioms of this type tend to be used more by older people. I doubt if many English-speaking 17-year-olds would use these expressions in natural conversation.

The use of informal expressions and idioms is regional and personal. They can vary from family to family. I suggest that you recognize and understand them, but not try to use them. In my own life... personally... living where I live in the northeast United States... I've heard and used "my lips are sealed," "keep it under wraps," and "let the cat out of the bag." I've heard #4 but only in the form "a little birdie told me," not "dicky bird." "My lips are sealed" and "a little birdie told me" are teasing and humorous. "My lips are sealed" would be said in an exaggeratedly formal way. The idea is that you are making a very formal pledge to keep a completely trivial secret. "Oops, I have to get rid of that doughnut bag, I promised my wife I'd quit buying a doughnut every day. Don't tell her!" "Fear not! My lips are sealed!" "Keep it under wraps" and "keep it to yourself" are straightforward and serious. I've never heard or used "mum's the word," to me it's only something I've read in books.

I'm from England. I've heard them all. 4 is now unusual but the rest are common. They are used mostly in speech so if you want to use them yourself, I recommend finding dialogues which contain them.