Hiya!
Something that I've been seeing a lot lately is that the party should be faced with encounters that they cannot win. That they should run. My question to you is how do you convey this information to the party without being ham-fisted about it?

Uh...you don't? I mean, it's NOT UP TO YOU TO SAVE THEM, simply put. Your question is like someone picking up a 1000pg mystery novel and the first page says "Synopsis: The butler did it, in the Kitchen, with the Candlestick. Enjoy!".
So, you do nothing. The Players will figure it out...or not. Either way, it's not your problem and certainly not your "job" to help them not die.
Now there are the obvious clues like the dragon being really really big or the player failing to penetrate the monster's armor after rolling a 19. But how would you subtly let your players know they're in over their heads. Have you ever found yourself in a situation where you just can't save the players from themselves?
Ok, I think you're doing it wrong.

Y'see...when you're sitting there doing the DM thing, explaining the situation in terms of what the PC's would sense (see, hear, smell, taste, touch), all that information is already "letting your Players know". If they don't recognize the danger, then either they are really not picking up on it for whatever reason...or you just need more practice describing stuff. Keep at it! You'll get there!
Tips: Tone of your voice and "pacing". These, imnsho, you just have to learn/develop. They can't be taught. There is a distinct difference between "The chamber is 40' square, with a vaulted ceiling, 20' or so overhead at it's central point in the middle of the room. The walls have faded frescos of Sir Lightheart slaying various foul creatures...a black dragon being decapitated, a demon being struck down by Sir Lighthearts legendary sword, 'Angle-Kiss', and another of the Evil Ursurper, King Rendwood kneeling in defeat before the knight. In the north west corner is an old Romanesque style couch and footstool. Upon the couch rests the bones of some humanoid, once dressed in fine clothes, now rotted and eaten away. A dust covered golden goblet lays on it's side, just out of reach of the skeletons outstretched hand. Slowly, to your horror, red-glowing embers start to form in it's dark eye-sockets!". ... ...and... ... "The 40' square, vaulted room has frescos on the wall, but your attention is drawn immediately to the skeleton on the small couch in the NW corner...as it's eye-sockets suddenly spark to un-life with a hellish red glow!".
The length of the description and the detail all set the "pacing" of the scene. In the first, it's more of a "slow burning horrific realization", and the second is more of a "sudden surprise of danger". Both descriptions will affect your Players differently. This is how you can "hint" at something very dangerous up ahead. Description, description length, and tone of voice.
In the first example, it is described with the Players being "horrified", but not "surprised"; meaning they are FAR more likely to react in a manner appropriate to the danger; they will think more carefully and have more time to assess the potential danger...given all the other potential hints at who...or what... lairs in this dungeon/ruin, they are more apt to say "Yup! That's a Lich! RUN!". But if the second description is used, IME, Players will tend to react 'instinctively'...and, for many adventurers, this is "Get it before it can do something!", and not fully appreciate the situation for what it is.
So...as I said. "Pacing" of your descriptions. This is the BEST way that I have found to help "hint" (if you can call it that) that something overly-dangerous is up ahead.
^_^
Paul L. Ming