Well my mom says I'm too young to visit because I am 16. (even though she went too Europe at 16) She also argues that she doesn't know his parents, yet when I try to get them to talk she makes no effort to communicate. I would pay my own way as I have my own job, and my boyfriends parents (very religious) offered to house me with his 3 other pretty rad brothers. I feel if I can't see him our relationship will fail. Please help. ^^^^
Once I found out that my boyfriend was going to be moving away, I would have made sure that our parents had met. Why, you might ask? I think you have now found out why. If this were me, I would bring my computer to a common area in the house and Skype / Facetime the boyfriend and/or parents where a parent could overhear and possibly join in the conversation.
In addition, I certainly wouldn't add more drama to this situation by constantly nagging and whining about going to see your boyfriend. That's what an immature daughter would do - whine when she can't get her way.
Ask mom and dad - in a nice and respectful way - what would it take for them to be comfortable in allowing me to go visit the boyfriend. And if they continue to say no, accept the no with good grace.
There are many ways that you can try and keep communication going with him but it will take time and effort from both sides.
Danae has given you several good ideas. The only thing I can add to this is Mom rules.