and I've looked down each column of the image and added up the values: then do the units change? My thinking is that I'm taking something that is measured per steradian (which is a solid angle) and integrated it along a single axis, which would be in degrees. Would this make the units of my graph now MJ per radian? Or am I simply adding values in MJ per sr, so the units don't change?
You could say "MJ in bins of x degrees in l" where x is the degrees spanned by a pixel. Or, you could divide the fluxes by the steradians in each column and keep it MJ/sr or "Mean MJ/sr within longitudinal bins". Now the width of the bins is not important as long as they are small.