Which map projection has the least distortion mercator, lunar, goode, or, oblique

A mercator is totally accurate at the equator and gets worse when moving toward the poles. The goode is a mercator with much of the inaccuracy left out. It looks like an orange would look if you just took the skin off and smashed it as flat as you could. The distortion comes from the part that wouldn't go flat. Oblique just means the observer point of view isn't along the equator or looking down from a pole.

I don't know what a lunar projection is. If I had to make a guess, it would be that a lunar projection is what the earth looks like from the moon. In this case, at the single point on the earth's surface nearest the moon, there is no distortion. As one moved away from that center point in any direction, there is more distortion. So, lunar would be the most distorted further away from the closest point.

If you are talking about a world map, then goode has less distortion than the mercator or the lunar. If you are talking about a map of some relatively small area, say the state of Rhode Island, then an oblique map centered over the center of the state with a mercator projection would have no distortion, say on an east/west line through the state and very little distortion out to the edges of the state north and south. A goode would theoretically have less distortion, but you wouldn't be able to discern that difference. A lunar projection might have less distortion N/S and more E/W. My guess is that it would average out to be about the same.

Look up "map projection" on Wiki for more info.