One day my phone notifications just like stopped popping up. If I have my phone in my pocket and I would get a text or something, my phone would vibrate. Now it doesn't, so if I have a text I have to click the home button and it will show up on my lock screen but it doesn't make a noise or vibrate. If someone calls me I miss it because it doesn't ring. It's been doing this for a while and I thought I could deal with it but it's just annoying me now. I have checked my settings to make sure all my ringers are in and stuff and it says it's on so I'm not see what's wrong. When I'm actually on my phone and using it the notification will pop up, make and noise, and vibrate, it's only when it's off (not completely off) so if you have any ideas please let me know. It's an iPhone 5c by the way.

Have you actually completely shut it off and did a cold restart?

IF it was really off....it wouldn't vibrate or do anything..(you are talking about a standby mode which isn't off)..it would be an inert lump doing nothing at that point until its restarted/turned back on.