I don't think auditing will show you who activates or deactivates features.
But you could set log level to verbose, like this:
Set-SPLogLevel -TraceSeverity Verbose -EventSeverity Verbose
and then you could look for __Current User=...*, although I can not guarantee it will work, and setting log level to verbose will of course also have its implications.
// Do ajax here
then you could either use Client Object Model to get the current user or even just post directly to a WCF Service, which should know what users is calling it, and then log this information in any way you want. For example using SPLog.