With the playoffs not yet concluded, the NFL has yet to officially determine the complete 2014 NFL draft order, but we can more or less tell where the Titans will be picking. By my estimates, the Titans currently hold the following picks in the draft:
1st round, 11th pick, 11th overall (own)
2nd round, 10th pick, 42nd overall (own)
4th round, 12th pick (own)
5th round, 11th pick (own)
6th round, 10th pick (own)
7th round, 13th pick (own)
Barring something unexpected, the pick in the first round will be the 11th overall pick and the pick in the second round will be the 42nd overall pick. The exact position of the fourth through seventh round picks will be affected by the NFL's awarding of compensatory picks; my preliminary estimate is those will end up being the 111th, 146th, 180th, and 221st picks. The Titans currently hold six of their seven original selections, having traded their third-round pick (13th of the round, likely to be 77th overall) to the San Francisco 49ers when they traded up to select Justin Hunter in the 2013 draft.
The Titans will almost certainly not be awarded any compensatory picks due to their free agent signings last year.
When there are updates to the Titans' picks, I will update this post.