Pretty much anyplace you'd use sheet aluminum outside. Think roofing and home exterior finish work... they are used to attach the aluminum trim used to surround the roof, or on a home with aluminum siding with trim around windows. I think I've seen them in screen door frame construction as well. 3" screws would be perfect for making frames from extruded aluminum at the miter joint. Screen doors, or perhaps window frames? They would be handy for connecting aluminum down spouts and drain pipe segments together as well. (oops.. not true for 3" long screws!)
In fact working on aluminum drain pipe / downspouts would be my first guess as to what your box of screws was originally purchased for. Let me guess, are the heads of the screws painted (typically black, white or brown) ? Whoa... I just read our note again.. 3" screws sounds like something you'd use to hold the rain gutter to the house. Let me see if I can find a photo. That is a very odd length. Perhaps something like this? Normally I see long aluminum nails used (4 or 5" in length), but what you are describing could be used in the following design:
You'd use them anyplace where there can be galvanic corrosion caused by the use of different materials exposed to the weather.
Remember in the old days, when they made aluminum framed windows for homes? How about the tacky aluminum awnings that used to be so popular in the 1950's and 60's? The other place you might see then is in aluminum body motor home and trailer construction. Aluminum screws with aluminum material is pretty safe. On the other hand their strength is somewhat suspect.
