The phrase "awkward sense" is correct and usable in written English.
It can be used to describe a feeling or perception that is uncomfortable or not quite right in a particular context.
Example: "She had an awkward sense that she was being watched during the meeting."
Alternatives: "uncomfortable feeling" or "strange perception".
Sergio had a buzz cut, a square jaw, and an awkward sense of humor.
Unfortunately, he rarely performs in English - you're just going to have to learn Lithuanian if you want to appreciate his awkward sense of humour!
Once you get past the name of Chris Peters and Shane Gabler's label, Creatures of the Wind, and embrace their awkward sense of femininity, things start to make sense.
So anyway, we went to see the Los Angelinos play their first concert in Europe last night, in London, where they fought their own awkward sense of displacement, dealing with two sets of expectations.
That shift in perspective might be startling enough, but the movie goes one step further by charting the effect that Ms. Schwartz's transformation has on her family members and the awkward sense in which her embrace of a biracial identity might be seen as a repudiation of them.
Of course, there will be snags, mistakes, blunders and an awkward sense of what everyone is doing.
Shrode finds the situation reliably awkward, sensing a whiff of pity riding on the backside of flattery.
If you shy away from connecting, the interviewer may feel awkward and sense that you're not in it to win it.
They share "gee-whiz language, hokey humor, awkward stage presence, sense of entitlement and noblesse oblige".
Though the fit with this hipster lite-blogging, photo-heavy platform could seem a little awkward, it makes sense in the context of Yahoo's ad strategy.
After spending years in Sacramento, Didion's father, an army finance officer, moved the family around, but Didion thought of herself as pure Californian: individualist, resistant to group mentalities, "awkward" in the sense of not wanting to join in.
