There are two schools of thought when it comes to using our own earth calendar (the Gregorian calendar, also known as the civil calendar--the accepted standard.) One is that, since we're using our own language, (and I'm going to use English as the standard here, since that is what I'M writing in) use it in its entirety. That includes the days of the week, the months of the year, the seasons and even "clock" termininology. This is the easier method, and probably the most consistent.
The second school of thought is to avoid the terminology the way you would idiom. This is where things get sticky, because, short of inventing your own way of measuring time from seconds to seasonal cycles, it's impossible to avoid them completely. For example, we all know that our Wednesday comes from Norse mythology: Odin's Day--Woden's Day--Wednesday. How, you ask, can there be a Wednesday in a world in which Odin doesn't exist? Grand--no Wednesday. So...does your world even have seven day weeks to appropriately name? Does it even measure time in weeks? How about the hours in a day? How long is a day? What about seasons? Does your world have the equivalanet of winter, spring, summer and fall? Or is it a tropical culture? And if so, does it exist within a civilization big enough to know what winter is in concept if not in reality?
See what I mean? Much harder.
While the first school of thought is easier by far, and, if done with consistency and no apologies, will cause the least amount of controversy among your readers, the second will enrich your world, make it unique.
Do you want to use minutes and hours, but not week or month? Does your world have all four seasons?Use your world's culture to create the names of those spans of time you want to make unique--like Woden's Day. And, like the heading on this post, create those idioms and sayings that will go along with your world calendar. Remember that holidays is a joining of holy + days, create and use them accordingly to give the feel of those your reader will recognize from their own existence. (For example, in Karin Gastreich's Eolyn, there are festivals and rituals that equate to, but are not exactly like, Christmas and Beltane.)
As for me, I prefer the second method. How about you? As a reader? As a writer?