What helped me get my inventory under control was a few things.
The first was not keeping any non-named items other than crafted blueshine/everbright, or in special cases light blue-bordered items (mainly weapons, but even then I don't keep very many of those). If it doesn't meet this criteria, it's getting broken down or junked.
The next was only keeping useful mythic and/or reaper boosted named items. If it's standard it's getting fed/junked; the only exceptions being raid items, rare/chase items, and/or artifacts I know are actually useful. When it comes to reaper items, unless I'm really sure I'm going to use it, it'll get fragmented for boosting other useful items (again, unless it's a rare/chase).
Thirdly was that cosmetics are generally tossed if I know I can get a fresh set later. Having a cosmetic mule is never a bad thing if you have the character slots. (It would be nice if SSG to go back and retroactively add a Feywild vendor like they did with Sharn, just because I'm lazy and don't want to make a toon only to destroy it just to pull cosmetics off it, but that's just me.)
Everyone has different organizational methods, but I tend to keep non-BTC pack items on specific mules if I can. One mule has IoD, one has Myth, one has Lamordia and so on. I generally put armors and/or cosmetics from that pack on that mule for quicker identification (though I generally know the names of which toon has what by now.). Since I only keep specific types of gear, this helps keep my mules' inventories relatively clear.
When it comes to crafting storage for filigrees and ingredients, I keep only useful ingredients and rare filigrees, the rest get junked. (Some people keep BTA bags with stuff like this in them instead of/in addition to their crafting storage, and that's another solution.)
All this has made it so my player toons have very small amounts of inventory taken, and I have pages of empty inventory while I'm playing (my individual and shared bank have a lot of open space as well). It makes TR-ing a much faster process when you maybe have to move less than 100 items rather than a couple hundred.