Thanks for the debugging info and steps you took 
What you’ve done means the server is running and DNS/hosts file is working at least.
Here’s the next steps you can take:
vagrant sshsudo service nginx status
Hopefully that says it’s not running since that’s easier to debug.
If it’s not running, you can run sudo nginx -t to see if there’s any configuration issues. And might as well try to run sudo service nginx start or sudo service nginx restart and see if that gets it running.