Spokes come in different gages. Straight 14g would be the strongest (but you may already have these). However, there are lots of other factors that could be causing the spoke failures. A big guy should have a wheel with at least 36 spokes, laced 3 or 4 cross. If this is a low to moderate-priced comfort bike, it may simply come with poor quality components. Cheap hubs may have flanges that are narrower than the spoke elbow, or spoke holes that allow the spoke ends to move. These and other factors could stress the spokes and cause failure. Rebuilding with washers under the spoke ends could help in some case. Or replacing the wheel may be the better option. I'd suggest taking the wheel to your LBS and discussing the spoke failures to see if they can spot an obvious reason. If spoke tension is poor they could correct that for a moderate price. It is unusual for spokes to fail on the left side.
Oil is good, grease is better.
2007 Peter Mooney w/S&S couplers/Terry Butterfly
1993 Bridgestone MB-3/Avocet O2 Air 40W
1980 Columbus Frame with 1970 Campy parts
1954 Raleigh 3-speed/Brooks B72