I think that these following expressions have quite similar meaning :
- Take care
- Be careful
- I want to warn you
Are they synonym, or is there any subtle difference of strength? Does other variations exist?
"I want to warn you" or "I am warning you" are both subtly stronger than "be careful". "Be careful" is what you might say to a child whose glass of juice is dangerously close to the edge of a table, or who is ice skating too fast. "I am warning you" is what you might say to someone who is making a bad decision that will lead to their getting injured somehow.
"Be careful" is encouraging someone to behave cautiously. You can also make "take care" work that way: "Take care not to stub your toe." They mean approximately the same thing. ("Take care" is also used idiomatically to wish someone well, often at the end of a conversation. "It was nice to talk to you. Take care! Bye!")
"I'm warning you" is more of an admonishment. You might use it when you think the person you're speaking to isn't going to listen to you, or isn't aware of the danger - or isn't going to be careful. It is more severe in tone than either "take care" or "be careful".
Similar meanings? Perhaps.
Suppose someone is going down a steep flight of stairs. I might say:
Be careful going down those steps.
I suppose I could say either of these:
Take care when going down those steps.
I want to warn you about those steps – they're steep.
but neither of those sound as natural to me.
Take care is also used as an expression when leaving each other.
Have a good night, Bob.
You, too. Take care.
When saying something along the lines of "Be careful!" I think I want to warn you sounds a bit stilted. When advising someone to use caution, I'd be more inclined to say, I should warn you, as in:
I should warn you – they have a mean dog.
which would be similar to:
Be careful – they have a mean dog.
But the two expressions aren't always interchangeable. A professor might tell his students:
I want to warn you, the last problem on the final exam will be difficult. Be careful when you're working through it.
The warning isn't so much a safety exhortation, it's more of an announcement. And be careful in this context isn't about safety precautions, but about not being careless in your work, lest you make an error.
In short, I think there is a lot of room for variation depending on the context. It's probably too much to cover in just one question, but perhaps a few more answers could help you get the feel of it.