How may I use narrow space between fences?

Thats about all that you can really do with it. You cant really grow too many things in there.....I think it would be fun to watch ducks play in the swale.

As long as none of your neighbours will complain about them, I would go with the ducks. They will also keep the weeds down.

I'd grow some sort of vining vegetable.  Maybe snow peas. Or how about grape vines.  If it is shady, you should still be able to grow raspberries (the erect kind that don't spread by runners).  Blackberries would be even better, but of you are Canada, it might be too cold for them.

Pawpaw trees require shade when they are young and they will grow and fruit in cold weather.

To me, it seems beyond rude to pen noisy animals as close to the neighbor's property as you could possible get them.

A nice vine would give you some privacy from the neighbors.  If you could get some food off of it, more the better.

I'd put down black plastic mulch to eliminate weeds and warm the soil for whatever you decide to grow.

I think you might come to regret it if you encourage stray cats to live at your place.  You'll soon be overrun with cats, and they will be spraying foul smelling urine all over your property and your neighbor's property and digging and pooping in all your flower beds.

Run the weed wacker and mower through there.  Then as Oregon Blues mentioned get some weed block and roll it out along there.  That will get rid of the weeds. 

Id look at doing snow peas, then when those are slowing down, put in some pole beans like Kentucky Wonders and go and pick them all summer long.  Grapes would be another good choice.  Heck with area that big you could easily do all those and have room left over.  You could even try to get creative and attach some kind of stock wire fencing to the existing fence and try to trellis up some cucumbers or even a couple of indeterminate heirloom tomatoes. 

Once the plants break through the ground mulch and help train them onto the fence.  If its as well watered as you say you'll have plenty of veggies for you and your neighbors.

Another thought to help take up some space would be a climbing rose.  Just had that after I hit the submit button.  Keep us posted please

Are you looking for a 'permanet' installation or simply temporary?  I ask, as the annual veggies would be temporary - like cucumbers or melons or squashes (our pumpkin plants are outrageously large and climbers!). 

If you're looking for permanent, do you want food for you or for the critters?  You could plant trumpet vine and attract hummingbirds, milkweed and other 'natives' to invite butterflies, moths and birds galore, grapes for you or even fruit tree espilliers (sp?) - the kind of fruit tree that you can train up to grow against a wall, commonly apples and cherries are done this way. 

We have about 120' of grapevines planted sometime in the 1940's.  With care and annual pruning, we've gotten bumper crops for the past 3 years.  But, the vines had been neglected by previous owner (40yrs here), so it took a good 5yrs before the vines were productive again.  If you go this route, select a grape that you want a lot of!  Ours make excellent jelly, but are nasty for eating.  Although the birds and rabbits have no qualms about snitching them!  So pick carefully!

Only go for the trumpet vine beside the neighbor's fence idea, if you REALLY hate your neighbor and want to punish them. Yes they are pretty....but they are rampantly suckering and get trunks as thick as small trees that will chew through a fence in short order. I love trumpet vine, but only in a place that the lawnmower keeps the suckers under control. I am fight a fence trumpet vine right now. It was planted on the corner of my porch by someone decades ago....it has dug its way under my cement sidewalk and comes up happily along the fence-row now. It is indomitable!

I would grow herbs. Especially if the soil is poor and on the sandy or well drained side. Or a small strip of native/wildflowers.