Can I have an odd-number of teams without any bye weeks?

You can set up an ownerless "ghost" or "dummy" as then edit its boxscore after each week to assign it any score you want. Some leagues assign the dummy team the league average score.

1. Create a new team from League >> Settings >> Create a New Team
2. After the end of each week, edit boxscores from League >> Edit Past Box Score
3. Find the ghost team's matchup, and assign it the desired number of points.