[ ] and { } and ( ) are completely different in Mathematica. Using one when Mathematica expects another will cause great confusion. I have made a number of changes to try to get this to work. Is this now correct? Does this solve the first part of your problem?

Plot[Evaluate@Table[PDF[GammaDistribution[Alpha, Beta], x],
 {Alpha, {0.31938, .267499, .1829}}, {Beta, {0.31867, .268469, 9998}}], {x, 0, 20}, Filling -> Axis]

Entering example Mathematica code on separate lines, highlighting that with the mouse and then tapping Ctrl-K will keep the forum software from doing some damage to your code.