Yes, you can obtain TN status at any POE and then return to Canada. Then return to US a few days later to start your job.
You do not hand in your I-94 when you return to Canada.
Your TN status is linked to you passport number, so it is all electronic, in the CBP system.
The only time you hand in your I-94 is when you return Canada with no intention of returning to US on TN status (ie. after quitting job in US).
In 2015 I obtained job offer for engineering job in California. I requested TN status at Queenston/Lewiston bridge in Niagara falls New York state area, (as well as TD for family), a few days before I flew from YYZ to LAX. I stayed in US for a few hours, opened US bank account, eat lunch at restaurant, then returned to Canada.
The CBP officer did not ask why I was applying for TN in Niagara Falls, when my job was in California. They are familiar with many Canadians from the Greater Toronto Area requesting TN status for jobs in US.
Odensburg should be fine as well. Relax.