To be honest I've never thought about it before, but I will add some observations:
"Feelings" tend to be used when we're talking in general about our emotional state. For example:
- "I share your feelings on this topic"
- "Her feelings are as important as yours!"
- "You really hurt his feelings"
"Feeling" tends to be more specific, often using "that" or "about", and seems to most often come with the verb 'to have' along with an observation or opinion (rather than something emotional):
- "I have the feeling that I'm being watched"
- "I have a feeling that we're going to win the World Cup"
- "I have a good feeling about my job interview"
As the subject of a sentence, it almost always take the form of "My feeling is that..." followed by an opinion. Or something emotional would again refer to the plural: "My feelings were hurt yesterday".
Sentiment and sentiments have a bit more of a distant/formal feeling about them, and are almost always about opinion, rather than emotions. For example you can have hurt feelings, but not hurt sentiments.
If the people are plural, then the verb is the only thing changing. To take my examples above:
- "I share your feelings on this topic"
- "Her feelings are as important as yours!" becomes "Their feelings are as important as yours"
- "You really hurt his feelings" becomes "They really hurt our feelings"
- "I have the feeling that I'm being watched" becomes "They have the feeling that they're being watched"
- "I have a feeling that we're going to win the World Cup" becomes "They have a feeling that they're going to win the World Cup"
- "I have a good feeling about my job interview" becomes "We have a good feeling about her job interview" (the only reason I changed it to 'her' is because multiple people don't normally interview for a job)
I hope that helps!