If my Lugia EX knocks out an opponent's Garbodor with the "Garbotoxin" Ability and a tool attached, does Lugia EX's "Overflow" Ability turn on in time for it to take two prizes?
Nope, Garbotoxin is still active when Garbodor is KO'd, so Lugia EX does not get to take 1 more prize card for Overflow.
Source: TPCi Rules Team (2013-02-28)

Relevant cards

Note: All applicable cards may not be listed below.
BW11_102
BW11_68
BW6_54
BW8_108
BW8_134
BW9_119
BWP_BW83
BWP_BW83
XY9_57