Nguồn tin Việt Nam bằng tiếng Anh
Something that is as tough as woodpecker lips is very strong, resilient, etc.
A camel's nose is a small, seemingly harmless act that can have undesirable consequences if allowed.
If someone is off the leash, they are no longer restricted or controlled.
If you keep someone on a short lease, you restrict them and control what they do.
(On a tight leash is also used.)
If someone is straining at the leash, they really want to do something that they are prevented from doing at the moment.