I assume every anecdote would have it's own plot, conflict and resolution? Otherwise there would really be no point in telling them.
There are four types of stories: world based, event based, character based and idea based. While it's true that all stories need to have some kind of a plot to be interesting, the plot is not the main focus of every type.
Take Lord of the Rings, for example. It has an engaging plot, that's for sure, but the book isn't really about the war against Sauron or the destruction of the ring. If it were, the book would stop after the ring was destroyed, but instead we have the whole cleaning of the Shire afterwards, we have Bilbo's birthday at the beginning, we have Tom Bombadil... That's because it's not an event based story, it's world based. Even the characters are little more than stereotypes, with Legolas, Gimli, Merry, Pippin being simple representations for their races, with very little character debt or development. It's because the characters are not as important as the world. But the world is painted with amazing care and detail.
Every Agatha Christie novel is an event based story. There was a murder, and the plot revolves around that. The setting and the characters are not as important as the conflict and the resolution - finding out who the killer is. She has a few wacky characters, but we're not reading it for them, we're reading to find out who did it. In this type of story the plot is the most important, because no one wants to read a who-done-it that is illogical or where you figure out on the first page that the butler did it. A good plot is what drives this type of story.
Character based stories need not much explaining. I'm sure we all ran into a novel that is not so much on the plot side, but we kept reading because the characters are engaging. Who watches House for the weird medical cases? We all watched it to see what insane things he'll pull off next. The readers will close their eyes on a weak plot if the characters are cool enough.
The idea story would be Orwell's Animal Farm or Nineteen Eighty-Four, where the plot is just a way to present the idea, to entice the reader rather than beat him over the head with that idea. The plot is in the service of the idea.
From your description, you have either an idea based story or a world based story, or a combination of the two. Which ever it is, the plot is not the central element of your story. There has to be some plot, no one will read it otherwise. You need to pick a plot, or a series of small plots, that will best represent your world or your idea. It doesn't have to be something complex. Plot of the Animal Farm is pretty simple - you have animals on a farm that have rebelled against their human owner and took over the farm. Then one of the pigs installs a dictatorship and everything goes downhill. It's not a terribly dynamic or original plot, it's actually just author's representation of the events in Soviet Union at the time. It doesn't have to be original, it just needs to represent the idea well. It could be something classical, why not? It could be a representation of a historical event. You just need to figure out what you want to show, and shape the plot accordingly.