Postgresql User not connecting to Database (Nginx Django Gunicorn)

Your application is trying to connect to PostgreSQL using a password authentication method, but in your pg_hba.conf file, the connection type is matching the md5 method so it's expecting a md5 authentication. We can see this in your log messages

2017-09-01 11:42:17 UTC [16320-1] vpusr@vpdb FATAL:  password authentication failed for user "vpusr"
2017-09-01 11:42:17 UTC [16320-2] vpusr@vpdb DETAIL:  Connection matched pg_hba.conf line 92: "host    all             all             127.0.0.1/32            md5"

Locate your pg_hba.conf file inside your PostgreSQL data directory, vim the pg_hba.conf file and update the line

host    all             all             127.0.0.1/32            md5

and change it to

host    all             all             127.0.0.1/32            password

and then restart your PostgreSQL service

[root@server] service postgresql restart

and then try to authenticate again

To expand on the other messages you are seeing, when you run the command: sudo -u postgres psql -U vpusr vpdb you are not passing the -h <host> parameter, so the connection will attempt to match the line

local    all             all             127.0.0.1/32            <method>

so you will need to check which method of authentication it expects for local connections and authenticate that way, or else pass the -h <host> parameter, and then it will match your line

host    all             all             127.0.0.1/32            password

which means you can then enter your password when prompted, or else change your connection string to

sudo -u postgres -c "PGPASSWORD=<password>;psql -h localhost -U vpusr vpdb"