When I ssh in to my vagrant vm, I can change permissions of files and folders above and outside the vagrant user folder, and for files within the vagrant user folder. But ca
VirtualBox doesn't allow changing the owner/permissions for synced folders.
You can change it in the Vagrant file (as answered by others).
Consider changing the owner instead of the group.
Consider also that - if done so that your server can write to files - your server is likely called www-data instead of httpd. Use ps aux | grep nginx
[or apache / lighthttpd] to check.
There are some other options:
config.vm.synced_folder "/var/www/", type: "rsync"
config.vm.synced_folder "/var/www/", mount_options: ["dmode=777", "fmode=666"]
These answers are better described by Ryan Sechreset and Jeremy Kendall.