As far as which is more natural and which would be most widely said, I'd say that, generally speaking, the simplest possible choice is usually best in English. I'd probably say something to the effect of: This should be very easy for you; why would/do you need my help? (by the way, easy is a flat adverb, meaning that it has an adverbial form with or without the -ly suffix; sometimes flat adverbs sound better, but both are generally acceptable)
These phrases have slightly different meanings, so it's more an issue of both the context and what you mean to express than it is of one being more natural to native speakers than the other.
With the modal verbs can and should, can makes a more definitive statement about your abilities than should does. It's a stronger or more emphatic statement in other words.
In these examples, should suggests that you likely are able to do it with little effort, whereas can implies that you are almost certainly able to easily do it without help. In other words, should is more like ought to be able to.
And, as far as placement goes, it's generally best to place adverbs as close to the word they're modifying as possible; while the difference is extremely subtle, there is an ever-so-slight change in meaning when easily is moved around. Adverbs are fairly flexible when it comes to sentence construction, so you should try to place them where they are least ambiguous.
Regardless of how you construct them, you would place emphasis on easily in speech (hence both the bold and italicized text below)
You easily can get it done; why ask for help?
This essentially means that you could handily complete the task without help. Here it modifies can, meaning that you are able to quickly get it done. In other words: Without question, you can complete this task without my help, so why have you bothered to ask?
You can easily get it done! Why would you need to ask for help?
This basically says, You could very well complete this on your own, so why have you asked for my help? It's also modifying can here, in the sense that you can easily (effortlessly) complete it without assistance. To me, this is somewhat stronger than the previous example. It puts more emphasis on the modal.
You can get it done easily; why ask for help?
This is another way of saying: You are able complete this with little difficulty or quickly. When you move it to the end of the sentence, easily modifies done. How will you be able to complete it (i.e. get it done)? Easily/Handily.
Easily [Essentially/Clearly/Obviously/Without doubt/Unquestioningly], you can get it done by yourself, so why have you asked me for my help?
Easily is being used as a sentence adverb modifying the entire statement. Without question/By far, you can complete it yourself with little effort.
You should get it done easily; why would you need ask for help?
This one is the most significantly different from the others. This statement/rhetorical question, in essence, means that you probably can get it done easily, or that, more likely than not, you would/could be able to do it easily.
In this example, the speaker could possibly be mistaken in assuming that you can get it done easily; using should instead of can here is more like saying I could be wrong, but I think you'll be able to do this easily.
Side Note: This may have been unintentional (i.e. a typo), but there is a tiny issue with one of your examples (and this is being nit-picky/technical):
You should easily get it done, Why ask for help ?
Because these are two independent clauses, and because you are not using a conjunction to join them, this is a comma splice. That can easily be fixed by either adding the word so after the comma or replacing the comma with a semicolon (or a period).