I never stuttered - it was more terrifying social anxiety. There was a time where my legs felt rubbery I literally quaked in anxiety when giving a talk.
While I'm no great orator, I'm a long way from that now.
Not trying to project on you - but one of the big realization I made throughout this is that the things that I despised and dreaded most were also the things I was bad at. I convinced myself that parties were stupid for a variety of reasons - but at the end of the day I hated them because I didn't know how to handle them. Once I learned some of the basics there I started enjoying myself, and hey, now I look forward to house parties.
It absolutely is something you can work on. It takes a lot of time and very close attention, but it can be done.
I was the kid that nobody liked in middle school. I got beat up on a regular basis, everybody made fun of me, I had only a couple of friends and sometimes it seemed more like they tolerated me more than they enjoyed me, and I was basically in social hell. I was probably vaguely Aspergian - I fit basically all the symptoms - though the disease really wasn't all that well known back then.
When I switched to a new school, I decided that my only goal was to not be hated. I didn't care about being smart, I didn't care about passing my classes (we didn't have grades anyway), I didn't care about being popular...I just wanted the pain to stop. And so I basically shut up and observed. I watched how the other kids interacted with each other. I took note of what they were interested in, what got them excited. I purposefully tried to hide my intelligence, though my teachers basically shot that plan to hell when they pulled me out of algebra and told my classmates that the reason was because I scored a perfect score on the placement test.
When I did start interacting again, it was with "little" social interactions. Words of encouragement when they were struggling with a math problems. Questions about their favorite bands. Accepting their offers to come and hang out. In middle school, I had this hyper-competitive desire to be cool, and it resulted in a fair bit of self-aggrandizement that didn't exactly make me cool. In high school - at least early high school - I talked a lot less and listened a lot more.
And over time, it worked. I remember, about a month into high school, a classmate started making fun of me on the bus. Immediately, one of my other classmates piped up and said "Don't pick on Jon, he's cool." Problem solved, and I never really faced teasing after that.
I could try to put together a cribsheet of various social interaction rules I've learned if you're interested, but it may end up being rather long, so I'm not going to do it unless you think it'll help. Ask me for it if you want.
Being well liked among your coworkers and enjoying their company instead of dreading it everyday is a little bit too ineffable to work on.