I suspect issue with tmp file
Check ownership/permissions of that sock file
Correct method is to start with sysctl
When you try to start as mongod or sudo mongod it uses different parameters
In first case it complained about tmp file
In second case it says no /data/db directory
So as root it is trying to bring up mongod but since /data/db dir is not exists it failed
As sysctl it tries to bring up mongodb as mongod user which is same as first case but it is failing as tmp file is most likely owned by root
So remove this file and start the service again