The Volts have struggled to get a good read on the Black Caps tweaker and laboured again yesterday.
Sodhi ripped through what remained of the resistance to take seven for 98 at Cobham Oval in Whangarei.
Otago had been in trouble at 137 for five at stumps on day one but recovered somewhat to reach 331.
Derek de Boorder led the fight back with 89, while Michael Rippon (47) and Jimmy Neesham (34) provided valuable support.
Northern Districts is 97 for three in reply.
The opening day was rain-affected with just under 50 overs lost on Saturday.
Otago rookie Josh Tasman-Jones was unable to grap his opportunity at the top of the order, holing out to a pull shot.
Hamish Rutherford (26) and Neil Broom (17) got starts which was more than out-of-form captain Rob Nicol could manage.
He scratched around for about half an hour before getting an edge through to the keeper off the bowling of Sodhi on three. He was averaging just 12 going into the game.
Anaru Kitchen provided the highlights for Otago with 57 from 94 deliveries. The innings featured some lovely drives down the ground and one audacious reverse sweep off Sodhi.
The Volts resumed yesterday with de Boorder on 13 and Neesham yet to score. The pair put on 68 for the sixth wicket to steer the visiting side out of a little trouble.
Rippon continued the resistance with a valuable 47 in an 109-run partnership with de Boorder.
Sodhi got the breakthrough but he has bowled a lot better balls. It was a long hop which Rippon swatted to the midwicket fielder.
Still, Otago had got past 300 and de Boorder was closing on his fifth first-class century.
But Sodhi stepped into the spotlight and trapped de Boorder in front for 89 to claim his 10th five-wicket bag.
It was his second consecutive five-wicket haul against the Volts and half his career five-wicket bags have been against the men from the South.
He celebrated with two more quick wickets to wrap up the Volts innings.
In Wellington, centuries from Luke Woodcock (147) and Malcolm Nofal (179) enabled the home side to post 530. In reply, Central Districts is 226 for three.
A career-best knock from Ken McClure has given Canterbury control of its match against Auckland.
McClure scored 210 as the defending champion declared at 485 for six on day two in Rangiora, having waited for wicketkeeper Cameron Fletcher (100 not out) to reach three figures.
McClure's nine-hour knock was his highest in three seasons of first class cricket and comprised plenty of running, with just 22 fours registered.
Auckland crawled to 57 for five off 46 overs in response, with Will Williams taking a remarkable three for 11 off 18 overs. - Additional reporting NZN
