Rowing > Running > Elliptical
Since you're all on the topic of losing weight, the rowing machine will work more muscle groups and burn more calories.
And the elliptical is not useless, I do all of the 3 above. You can set an ellipticals resistance just like you can set the speed on a treadmill. Saying the elliptical requires no effort because it uses momentum is like saying the treadmill requires no effort because you're walking on it at 1mph. Both can be set to a level that will burn calories. I sweat just as much as I run... I usually set it to a resistance of 13-15 whereas I run at an avg 6.5mph @ 2.5incline. And yes I use "impact" as my excuse to go on an elliptical because I don't want to run 5 days in a row, so I'd run every other day and do rowing/elliptical/stairs on the days in between.