My apologies I should have been more specific.
Viewing the top results on the server reveals the mysqld process using the CPU cycles the most. Which is why I'm looking at the DB queries at the time of load.
Yes the site is old. Thanks for the schema check suggestion, I'll look into that. I've only recently taken on more of a role with the Moodle support, I'm primarily an infrastructure guy so pardon my ignorance.
The server is a VMware virtual machine. Running 2x vCPU, 8GB RAM, Ubuntu 16.04.1 LTS. The disk underlying is a hybrid array of SSD/SAS running over NFS 10 Gbps. Number of users varies at any given time, but I'd say no more than 200 at once but the server is accessed by maybe 1000+ overall.
The my.cnf file has been tweaked a bit prior. I've attached a screenshot of the file output.