The match only got under way thanks to the effort of local volunteers who cleared the thick snow on the pitch and they were rewarded with three stunning first-half strikes from Oli, striker Febian Brandy and John Nutter on his 100th appearance for the club.
Gillingham hit the opener after just eight minutes when Mark Bentley headed a corner across goal for Oli to connect perfectly with a bicycle kick for his first goal of the season.
Brandy had already tested Owain Fon Williams before he got the second shortly before the half-hour mark, collecting Simeon Jackson’s lay off before surging past two challenges and burying the ball in the bottom corner.
Matters went from bad to worse for League One’s bottom side when Nutter connected perfectly with Kevin Maher’s cross for an angled volley in the 33rd minute.
But the Hatters did manage to net a consolation in the 66th minute thanks to Michael Rose’s excellent 25-yard strike. However, Stockport have now lost nine straight league games.