Gnar can build full tank and still do damage so I feel like Trinity Force, Brutalizer, Last Whisper, and Frozen Mallet are solely luxury items (when ahead get even more ahead); although Frozen Mallet can have its uses at kiting/chasing and Brutalizer might be worth it if your lane opponent is building heavy ar. If you're going to go Trinity Force build the Phage component first (at least on Gnar). By full tank I mean Randuin's, Sunfire, Thornmail, Frozen Heart, Tabi's vs heavy enemy ad comps, or Banshee's, Spirit Visage, Hexdrinker, QSS, Locket, Merc's vs heavy ap comps. Or a mixture of both types of tank items when vs mixed damage teams (maybe thow in a GA and/or Warmog's in such a scenario). And Volibear is pretty much the same as Gnar when building except maybe he can do more with Trinity Force (?)... you can also think about going for Righteous Glory on him too.
As for what order to build them in... that's entirely dependent on how you are doing in lane and how the game is going. Items that come to mind might be Hexdrinker and Spectre's if you want help vs bursty ap and deal with them back. Chain Vest and Warden's in general to deal with ad early on. Merc's or Tabi's depending on what you are fighting in lane or think you will need come team fights. Other than that just minor items into bigger items and build situationally as I'm sure you are already used to doing. Just get better at it.
EDIT: BTW, I wouldn't rush Black Cleaver on Gnar... keep the Brutalizer if your going to build it but don't complete till you got some tank items. And I don't think Blood Thirster should even be considered an item to build on Gnar. Not sure if Volibear jungle can afford going Trinity Force unlike Volibear Top.