Is More Grease To Your Elbow A Correct English Sentence?

"More grease to your elbow" is indeed a correct english sentence, more specifically an idiom. Coincidentally, the correct, or more common form, of this particular idiom is "more power to your elbow", which also shortens to "Power to you!". This is a way of praising someone's success. However, it mainly stems from the sentence describing when something needs "more elbow grease", or someone tells another to "put more elbow grease into it", meaning that a little harder work or effort is required - that someone could put more effort into a task.

• How is it used nowadays?

It is more commonly used to refer to a physical task at hand (judging by the physicality implied in the sentence), but has been used in other ways too. This is a nice contrast to the idea that there should be some tool or aid to make the job easier - as elbow grease doesn't exist, it's a nice way of postulating that a non-existant aid will make all the difference in the successful completion of a task.

It is a statement (saying) rather than a sentence, which is often used to encourage a person following some form of good work; wishing that the person continues the good works in future.

No.
It's more power to your elbow

one can grease a palm not an elbow

Oh, my God! There are so many English idioms. It seems it's impossible to remember all of them. I am not a native speaker. Can you imagine how much effort I make to understand such phrases? I have recently found a list of idioms with explanations that impressed me a lot. Look at the article here.