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My raspberries seem to be breeding as many flies, small green house flies, as they are berries. The also seem to leave a sticky residue. HELP!

Are you talking about the long-legged flies?
https://insects.tamu.edu/fieldguide/cimg231.html

It could be they are attracted to aphids you have on your leaves and trying to eat them. I've seen one eat a fungus gnat.
[img]https://img.photobucket.com/albums/v73/Butterflyhornet/MyPhotos/DSC_3476copy.jpg[/img]

Without a pic, it's kind of hard to call just what type of insect it is, but these sites may help you out:

[url=https://whatcom.wsu.edu/ag/comhort/nooksack/ipmweb/Insect_1_Sheet.html]Rassberry Pests (with pics)[/url]

[url=https://urbanext.illinois.edu/raspberries/insects.html]Rassberry Insects and Diseases[/url]

[url=https://www.extension.umn.edu/yardandgarden/ygbriefs/e216raspberry.html]Rassberry Insect Overview[/url]

Hope this helps .