I have an odd setup under my kitchen sink, and about 5 days ago my hot water pressure decreased to a trickle.

Here's the setup: There are 4 valves under the sink, a disposal, an "Omnifilter", and "replacement cartridge.

The top left valve is hot water and connects to the single handle faucet with a plastic into woven metal line. The top left right valve is cold water, connected to the faucet with a woven metal line.

The other valves seem to be connected to the water filter, which has its own faucet. One of these days it's gone--we don't use it. It takes water, by the way, from the top cold faucet.

So--what could be the issue. We have major lime issues here, and I am unable to remove the screen from the faucet, but I would think that would also effect the cold water pressure, and that is fine.

Thanks in advance :)

Sounds likesomeone doesn't flush his heater on a regular schedule and now mineral build up has been pulled up into system where it's now clogging the hot water outlet. First lets find out where the clog is and then I'll give you instructions on maintaining your heater.
Turn the water off to the hot water faucet and open it up. Look down in the seat to be sure it's clear with no trash in there. Place a washcloth over the open valve body and turn the water back on for a second. Strong stream coming out? If not then unscrew the supply line and see if there's pressure there. If not, shut the house down at the house shutoff and do the same thing with the supply shutoff valve. Somewhere along the line you should run into pressure.
Now for the water heater. For long life and fewer troubles you should keep your heater clear of mineral build-up by flushing on a regular schedule. Attach a hose to the boiler drain at the bottom of the tank. With the pressure on, open the boiler drain and let it run until the water runs clear. You will see a spurt of red,(rust) followed by white or yellow grains,(lime or calcium carbonate). This shouldn't take more then a few minutes. Do this monthly to keep it clear. . Don't forget to flush it out every month. Your heater will thank you for it. Hope this helps, Tom