It boosts his ultimate by quite a bit, it gives him CDR, which makes his short cooldowns even shorter, gives him health + magic resistance. Warmogs is just a huge stack of hp.
The CDR isn't much, and it doesn't matter if you don't have the HP to support rapid fire of your abilities anyway. You're not going to run Burning Agony on a Spirit Visage, that's for sure. The health is just a single Ruby Crystal. Like I said about the unique passive, it boosts his passive and ultimate heals very very little without base HP to build on, since it all works off percentages. A slightly higher percentage of a small number is still a small number. Now after you've built some HP, the boost from Spirit Visage amounts to a lot, but not until then. Yes, it is a core Mundo item, but that doesn't mean it does a lot on its own.
Warmogs is just a huge stack of HP, but when two of his abilities are driven by percentage of HP and three others spend HP as fuel, HP is basically Mundo's main stat. It's a no-brainer to put the best HP item in the game on him. Yes, it's expensive, but Mundo is also a good farmer and amazing at denying early game. I often have it in under 15 minutes. I once managed to build up 5000 hp by 25 min, and that was before they remade Warmog's.
I will often buy the MR component of Merc Treads and Spirit Visage early just because, like I said, AP Burst is your biggest threat early game. Usually I get MR right after Giant's Belt and Boots of Speed. The other benefits can wait until I've got the prerequisites for them to actually amount to something.
Mundo is (was?... I doubt my recent quitting announcement will stick, as usual... I'm just miffed about this recent patch) my main champion and has been for several months. I have hundreds of games with him.
My typical build order is
Regen Amulet
Giant's Belt or Ruby Crystal (whichever I can afford on my first trip back)
Boots of Speed
Null-Magic Mantle (2 if I'm facing an AP heavy team or a good AP harrasser in my lane)
Finish Warmogs
Finish Merc Treads and Spirit Visage (whichever I can afford or need first depending on the game)
Those are my core items. After that, I build whatever I need based on the match. Usually I go for Randuins or Force of Nature. If I'm facing a well-balanced team, I'll get both. If I'm surviving easily or got fed early, I'll start building some damage. Phantom Dancer is my favorite damage item on Mundo.