I have been climbing on the same draws for seven years now. The nylon is kinda fuzzy, and the rope-end 'biners are worn about a quarter of the way. Is it time to replace them? They seem strong, and I've seen worse draws at the anchors of a lot of sport crags.
Knowing when to replace your quickdraws is confounding. Fortunately, other people are inclined to notice before you do, especially when their hide is on the line, so if they say "I'm not climbing on that junk, what are you trying to kill me?" you should take the hint.
Look in the mirror, friend, and stop fixating on what the other boneheads are doing. Thinking that your sawed-through carabiners seem strong because you've seen worse is a dangerously misguided nugget of logic that sounds like something The Birthers would say.
Based on your description, your gear sounds like total crap. Why are you so reluctant to spend $12 per draw to replace them? Are you on food stamps? Seven-year-old nylon that has been kept in the bag and unused would still be fine, but yours by admission is kinda fuzzy. Nylon tat such as yours can be surprisingly strong, but it can also surprisingly break, and outside a lab test there's no way to know how that pendulum will swing. Consider this the Pascal's Wager of climbing, and hedge your bet by retiring them.
And those gnawed-on carabiners! They are obviously compromised structurally and their worn, sharp-edged grooves are death to ropes, and possibly you. Just recently in the Red River Gorge, a carabiner such as yours sliced a lead rope in two during a fall. Fortunately, that leader was only two bolts up a sport route and escaped with a minor head wound. Having a rope cut in half like this may be rare, but is obviously possible. More likely, the sharp edges of the carabiner will "sheath" your rope, skinning it faster than a hillbilly on a polecat.
To illustrate how easily a taut rope can be cut, Mammut once tensioned a single rope in their testing jig, then lightly touched the cord with a dull, plastic picnic knife. Bam! The rope literally exploded into two pieces. As proven by Mammut, the old adage that climbing ropes don't break, they cut, holds true even for today's pimped-out cords.
The simple fact that climbers write me every 15 minutes inquiring whether their worn and old gear needs replacing is as chilling as waking up one morning to discover that your bedsheets are strangely damp. If you are concerned enough to bother asking the question, assume that your gear is unfit for duty. That the question is asked even more often about gear at anchor stations is bat-shit crazy since anchor failure is catastrophic. Come on mayors! Get off your duffs and replace those relics, or just strip it and force the issue like Larry Flint did back in 1978. Either that, or land managers from the Gunks to Index will soon be paving their trails with our bones.