Overnight on 88, Kunal Saikia top-scored for Assam with a fine 135, while skipper KB Arun Karthik contributed 62 as they were bowled out in 121.5 overs at Rajiv Gandhi International Stadium.
In reply, Odisha made a solid start with Govinda Poddar scoring an unbeaten 81 off 155 balls with the help of 10 boundaries and a six.
Subhranshu Senapati (34) was the other unbeaten batsman at stumps on the second day.
Assam were 224/5 when the stumps were drawn on the first day. Batting at number 10, seam bowler Abu Nechim chipped in with an useful 20.