Boy, I'm glad I stumbled onto this forum. My novel, too, has three moons. Fortunately for me, my dad spent some time as an astronomer's assistant, so I've gotten some good feedback on the plausibility issue.
I agree with Dommo... if the moons aren't that big, you shouldn't have much of an issue.
One of the big events in my book (for the inhabitants of the planet) is a triple eclipse. Obviously, they would have to be orbiting at different distances. Also, this would make measurements of time interesting. Here's what one of my beta readers (Actually, my incredibly technical little brother) had to say on the issue:
With three moons you could complicate the concept of a month, if you wanted, and have three overlapping lunar cycle measurements on the calendar. You could also do away with the month.
Then there’s the concept of the week which has its origin the creation week. You could invent some arbitrary division of time and, if you wanted to, attribute that division to something in the history or legend.
How many hours in a day on earth seems almost arbitrary (wiki it), and I think most sci-fi writers just stick with a familiar length of an hour and number of hours in a day unless they have some specific reason to change it. You could however adjust the starting point to sunrise instead of directly opposite noon as we do. To sound more fantasy fiction like, I wouldn’t say 5 o’clock. It’s probably better to say something like “the fifth hour (of the day)” or something like that.
Since seasons are dependent on the tilt of the planet and the orbit around the star, it makes perfect sense to have the same seasons we do. As for days in a year, well, they, of course, depend on the rotation of the planet and the orbital period of the planet. Now the Earth is in a very narrow range of distances from the sun that allows life to survive. However if the sun were bigger we’d have to be farther away and orbit slower or if it were smaller we’d have to be closer and orbit faster. So the orbital velocity depends of the size of the star. I recommend sticking to approximately Earth’s numbers but you can vary. As for identifying someone’s age, measuring by a season is a method that has been used here on earth and it makes perfect sense.
On a side note, in order to have all three moons be eclipsible the planet’s shadow needs to be big enough to account for their orbital tilts and varied distances. You don’t have to make any explicit indication in the book of this (or for a lot of the other stuff above) but it would help to have a larger planet and a larger sun so the planet can be farther from it. Just don’t forget about the increased gravity if you choose to enlarge the planet.