I would like to postpone or avoid the Civil War questline.

Once that begins, as I understand it, I lose the ability to clear many forts/dungeons because they are taken over by the factions and the bandits/monsters disappear. So to get the most out of the game I'd want to postpone that while I clear out those dungeons first.

Plus, frankly, both sides svck. I don't want to join either of them.

Is it possible to avoid advancement of the Civil War indefinitely? If not, what triggers it eventually?

yes, but if you don't do it, you have to deal with it at Season Unending

Which is not a bad thing. I greatly enjoy Season Unending and intentially get it every time.

Same for me. And I never did the Civil War.

What triggers Season Unending? Do I have control over it or is it triggered by passage of time or events beyond my control?

Its part of the main quest if you don't complete the Civil War.

It's in the main quest.
EDIT: Ninjad

Season unending triggers if there are 2 or more cities left to take in the civil war for your side and you reach a certain point in the main quest.

It triggers when you reach a certain point in the MQ, since you need the Jarl of Whiterun's help at that point and he won't give it unless there's a cease-fire in place.

I honestly wish the CW would progress on its own, however I can see why they didn't set it up that way since if it did there would be mass complaints from folks who put off joining only to find it had run its course in the interim.

Wow, Quadruple ninja in this thread.

You don't need to do any portion of the civil war to get this. You can ignore it completely. This quest is simply there because Jarl Balgruuf of Whiterun doesn't want imperials and stormcloaks at his walls when he has his guards occupied with protecting the city while you trap a dragon inside dragonsreach. Season Unending simply gets both sides to agree to leave Whiterun alone for a time.

I've done the entire MQ this way before.

But your right if you start the CW and only get part way through it, then Jarl Vignar Gray-Mane will say the same thing Jarl Balgruuf does.

Its a nice quest, gives you insight into both sides.

Keep in mind with "Season Unending", whoever you chose to escape Helgen with the game will consider you a part of that faction, and the opposing faction will begin to treat you with hostilities.

For example: Prior to completing that part of the MQ, you can go to any Imperial or Stormcloak camp and everyone is all nice and friendly, occasionally telling you to go join their side. But if you, say, escaped with Ralof then completed Season Unending, the Imperials at those camps will try and chase you off, and eventually attack.