Applied Energistics, my friend.
While a simple three blocks is enough to replace the entirety of your storage room, you can import functionality easily.
First, you're going to need an ME Controller. This costs you one diamond, plus some quartz, iron, and glass. By now, these shouldn't be a major challenge for you. This block will need power. Not a whole lot, but a steady power draw. But it can draw from MJ or EU, so if you want to think of it like a sorting machine with built in energy conversion, you can go ahead. By itself, it doesn't do anything, it's just required for the rest of the network to run.
Now then, I'm assuming you have barrels for those items which you have a whole boat-load, I'm guessing since you have routers already that you've got at least one extradimensional upgrade, and you don't want to deal with the hassle of moving all that crap around. This is not a problem. It's called a Storage Bus. It requires an ME Interface to craft, but it can pull from and store the item back in the barrel, no problem. AND the barrel is going to be the top priority automatically because the ME Network tries to put things in containers that already have them before putting them in containers without them.
For the chests... you can either use Storage Buses, or you can make a Disk Drive and store all that stuff on disk, with a huge savings in space. It would probably cost less to store it on disk, because you'd only need one Import Bus instead of a bunch of Storage Buses. But if you have an existing storage system you want to plug in, then you are quite capable of simply making the storage buses and hooking them directly up to the chests.
Then you'll want to build a Monitor, maybe even a Crafting Monitor (or perhaps both). Monitor just has to be hooked up to anything on the ME Network, so either the ME Controller directly or you can run cable to wherever you want to have access to everything. From the monitor, you can pull stuff out, insert stuff, sort... anything you'd really want to do with inventory. Fully searchable.
The Crafting Monitor is even better because it's got a crafting square. Now why is this so much better? Two synergistic reasons: 1) You can shift-? and automatically import a recipe, and 2) it will automatically draw from your ME Network. So you don't have to go hunting down a chest, pull out all the items you need, come back, and craft. You just shift-?, then click how many you want. Done.
A note about the storage: Higher size storage devices only increase the number of same items, not the number of different items. Each storage disk can store 63 unique items. However, you might end up with hundreds of each of those unique items, which is where the larger storage disks come in handy. It'll also store multiples of an item which doesn't normally stack. So you could have 64 (for example) 10k coolant cells, and it'll only take up one unique 'slot' (assuming none of them are damaged).