If I use Evosoda to evolve my Basic Pokemon into a Stage 1, can I then use Wally to further evolve it into a Stage 2 on that same turn.
Yes, but be careful of the order in which you play the cards. Wally says you can use it on a Pokemon that was put into play this turn, but Evosoda says you cannot use it on a Pokemon that was put into play this turn. So you can play Evosoda first then Wally, but you cannot play Wally then Evosoda (on the same Pokemon, of course).
Source: TPCi Rules Team (2017-03-16)

Relevant cards

Note: All applicable cards may not be listed below.
XY1_116
XY6_107
XY6_94