First, you set the variable $Date to "24 hours before now" :
$Date = [DateTime]::Now.AddHours(-24)
Then, you set the same variable $Date to another value which means "right now"
$Date = get-date -format 'MMMM-yyyy'
Get-Date means get a DateTime object for right now :
PS C:\> Get-Date 08 July 2014 12:36:05
The "-format 'MMMM-yyyy" at the end is just formatting the object representing "right now"
So, when you run :
Get-EventLog -computername $Computername "Application" -After $Date
You are asking for the events which occurred after "right now" , that's why you get nothing.
So, you need to remove the line :
$Date = get-date -format 'MMMM-yyyy'