"Shlep" or "Schlep" is a Yiddish word, literally meaning "to drag", but has a number of acquired meanings besides. As in English, where the word "drag" in its noun form ("a drag") has acquired the connotation of a nuisance or a chore, etc., shlep has a definite connotation of undesirable effort. I've heard it used two ways in this meaning - as a noun and as a verb. Shlep as a noun is almost directly equivalent to "a drag" or "a bit of an effort":

"Shall we make some dinner?
"Bit of a shlep. Let's get a pizza instead."

On top of this usage, shlep can also be used as a verb, meaning to do something that involves an undesirable or unpleasant effort, invariably involving going from one place to another:

"I've ordered a pizza, but they don't deliver. We'll have to shlep it all the way down there to pick it up."

As far as I can tell, shlep in this form is only used to describe exhausting and tedious movement. I've never heard shlep used as a verb to describe effort alone. If I were working hard all night on an essay, I would not say "I've been up all night shlepping" (which sounds a bit dubious, anyway).
There is a final usage I've heard which strikes me as being most probably a corruption of "shlep" and quite probably a very localised bit of slang, but worth including anyway - "shlepped", meaning to be exhausted or tired from great expenditure of effort (any kind):

"Pass me a beer, I'm shlepped."

Finally, here are a couple of other examples of how shlep might be used conversationally:

"You're late!"
"Late?! I've shlepped it all the way down here and that's all you can say?"

"I found out I had to attribute every quote, so I've been going over the paper all afternoon looking up the appropriate references."
"God, sounds like quite the shlep."