To be on the road means to be traveling. You often hear this used in reference to musical groups or other entertainers. They are "on the road," meaning they are traveling from place to place to put on their shows. You would say "I'm on the road," if you were traveling to or from work and someone called on your cellphone, for example. You could also say "I'm going to be on the road next week." if you were planning a trip of some sort.
Fork in the road means a time when it is necessary to make a decision.
It means to start a journey or to leave.
vocabulary of the road
Stuck in a rut is a phrase, but I am not sure if an idiom is the same thing as a phrase. You may be thinking of a cliche and "stuck in a RUT" is a cliche. "Stuck in a road" is neither cliche nor idiom.
It's not really an idiom. It means "what are you thinking about."
It is not an idiom, it means your nose is itching.
RFP is not an idiom. It's an abbreviation.
"Sieve" is not an idiom. See the related link.
It's not an idiom. It means the tip of your nostril.
idiom means expression like a page in a book
If you "take to the road," then you travel along it, so this idiom means that you started a journey of some sort.
"Where the rubber meets the road" is a phrase referring to vehicles -- when the rubber of their tires meets the road, you have movement. This idiom means "where the action is going to take place," and is generally used to mean some sort of decisive action.