Welcome to the forum - this is my standard advice to someone that already has a sparrow problem:
Here are some immediate things to do:
First - stop pulling the nests...let them build and become committed by laying their first egg. By then, you'll have this trap in hand (
http://purplemartin.org/shop/product_in ... d91ba95706
Then, you'll tear out the nest, but keep the nest bowl with the eggs into this trap and you'll catch the male or female right away.
Seriously, this works everytime for me.
When I first started trying to trap sparrows, I always panicked and didn't think deviously enough or like a 'hunter'. Now I have learned to have more patience and the end result is much better!
Here are some more steps to capturing sparrows:
1. Put out a repeating trap and put the feathers, or some of the old materials from the last nest tear outs in the bait tray of your trap. Sparrows LOVE feathers, white bread, popcorn & cracked corn (like the kind for chickens). Put some of all this inside the holding pen as well. Put the trap just below your martin house - off to the side 4-6 ft., up on a small platform that's about 1-2 ft. high. Put a couple of feathers just outside the trap so the sparrow can 'win' by grabbing a couple and he'll get cocky / comfortable around the trap.
2. Next - some work to camouflage your nestbox trap (linked above). Spray paint 2 pieces of cardboard with flat black paint. I cut these out to be the same size as the inside walls & back of my trap. That way, the sparrow can't see the wire sides or the depth of the cage..he'll think, 'man, it's really dark in here!'.
3. After the sparrows lay their first one or two eggs, carefully pull out the nest and find the nest cup holding the eggs. Gently tear the nest cup out (if you break the eggs - game over), keeping as little of the cup as possible, but enough to hold the eggs , and put that into your nestbox trap, on top of the trip lever. Put your nestbox trap back into the house in the same cavity and using some of the old nest material, camouflage the front of the trap when you close the nest cavity door.
4. It may take up to 30 minutes for either the male or female to re-enter the cavity...but they will....be patient!! After you catch the male or female that went in, if they didn't break all the eggs, reset the trap and wait for the other. *IF* you catch the female first, put her in the repeating trap in the holding pen. She's *bait* for future sparrows, so give her food & water & keep her alive. If you catch the male first, put him in the trap too,....maybe he'll attract the little woman to him.
5. I have had to resort to sticky traps with this same process, just putting the eggs on the trap, with lots of nest material around the edges. But let's not go there yet.....
Remember, when setting traps: sparrows "hop" around, they don't walk! AND sparrows are smart - never underestimate them...be smarter AND devious!
I will take a picture of my site and put it up here tonight. I started last year. I got one SY pair and two visitors. This year I have 3 ASY pair. It is so exciting. I am from Litchfield IL. 
