Sadly, I can't think of a weird situation that my characters. However, I can think of some awkward situations my character has been in.
In one of my drafts of my unfinished abandoned novel, I had a character who had a co-worker who constantly asked her out. She tells him no, but he doesn't take the rejection well and persistently asks her out. Once morning before going to work, she gets really nervous to the point of getting sick especially when she hears a city bus riding down the road. Why the bus? Because the young man who asks the main character out uses public transportation as his main mode of getting around town.
Another example of a weird or "awkward" situation is when a young woman in her early 30's is asked to lose weight in order to keep her job. This scenario can be considered controversial. She's not in the entertainment business, so some readers might ask, what's the big deal?
My character works at a doctor's office, for a CEO who wants all of the staff members to be healthy and in shape, and promote a healthy lifestyle; because after all, the organization promotes healthy living. I am still working on this story and will need to flush out some details. For now, my main character is staring at herself in the mirror reflecting on her years battling with her weight, forcing herself to face the truth about herself. She has to decide to lose weight and live healthier or just be content and miss out on opportunities.