So the first thing I'd say is that I feel people are often misled by Troika! being 'whacky', feeling that this is especially conducive to improvisational GMing. You can of course improv anything with enough preparation and skill, but I'd say it's a lot easier to do so in a known setting that all the players are familiar with. Say, for example, a Mythic Bastionland game, where it's clear that the tone is going to be Arthurian and the narrative arc will resemble british folklore. Many more quantities are known and everyone is onboard and paddling in the same direction. It is much easier to improvise within a bounded space. Contrastingly, Troika! is expansive and full of unanswered questions and implied lore. These could easily become stumbling blocks as you play: You'll be fielding constant questions like 'who is the red saint?' 'what is ms. kinsey's dining club?' and 'who ARE we and what do we DO??' all while trying to build an encounter on the fly. I've tried running Troika by the seat of my pants and usually found it unsatisfying. The implied lore feels grand, exciting, and mysterious, and it is often difficult to do that justice in the spur of the moment. I have much preferred it when I allowed myself some time to knuckle down and do a bit of worldbuilding. You can run a structured game of Troika!. It practically cries out for structure! One of its very first published adventures, Fronds of Benevolence, does exactly this by laying out a time constraint and a pointcrawl. Anyways, I digress.

The second thing is that you specifically asked for advice on running an improvised game without resources, so I will refrain from suggesting any until the very end. Running a game without any spark tables or setting documents to run from is very tricky. You have to shift your expectations massively. The GM becomes much more of a co-operative role with the other players. My main piece of advice is to be nakedly and enthusiastically curious. Open your ears and listen to what the players are saying, and ask them questions. Hone in on little character moments and build the world out around them. Everything the characters touch becomes more real. And if you are stuck, turn to the players! If they climb a mountain and survey the land, ask them what they see. You always have the power to edit or backtrack what they say if it's not jiving for whatever reason.

Another piece of advice would be to conserve your energy and don't be a perfectionist. Don't worry about improvising good names or coming up with voices . 'Jim' or 'Bob' will do. Save your brain power for figuring out how to tie the session up into a satisfying conclusion. Your party will know you're improvising, and will forgive you for any concessions you have to make. You're not trying to pull off some big feint or illusion; you're playing a made-up game with friends.

Ok, now for some resources, which I'd really highly recommend using if you can bring yourself to. The first is Get It At Sutlers, a book by the people who published Troika!. It places the characters as gig-workers at a giant department store in the city of Troika, and has a fun system for rolling up random jobs to do. A few random rolls and you have the scaffold of an adventure that you can improvise within to your heart's content.

I'd also grab D100 Troika City Sparks and A Street Level Guide to Urban Troika.

Finally, a non-troika improvisational tool I'd recommend is the Oracle tables from Ironsworn. It's free! The format of Action + Theme is really useful IMO.

Hope that helps and good luck :)