Group Policy

You can do that with a group policy by assigning a Startup(!) script to the machines in question (see http://technet.microsoft.com/en-us/library/cc770556.aspx).
Put the msp files into a share that allows the group "Domain Computers" Read access, and use this script as Startup (or Shutdown) script:

@echo off
setlocal enabledelayedexpansion
set SourceFolder=\\SomeServer\SomeShare\SomeFolder
for /l %%i in (3, 1, 6) do (
	set FlagFile=%WINDIR%\Temp\Hotfix%%i_Installation.flg
	if not exist "!FlagFile!" (
		set LogFile=%WINDIR%\Temp\Hotfix%%i_Installation.log
		msiexec.exe /update "%SourceFolder%\OrmedMIS_2013_Q4_Hotfix3.msp" /l*v "!LogFile!" /quiet /norestart
		if not errorlevel 1 (
			>"!FlagFile!" echo Installation success
		)
	)
)

Select allOpen in new window

The script uses a flag file to track the installation success; if there are files or registry keys that are set once a patch is installed, the check could be changed accordingly.
If the patches need longer than 10 minutes to install, you need to set another policy to extend the timeout: “Maximum wait time for Group Policy scripts” in “Computer Configuration\Administrative Templates\System\Scripts”.

An alternative might be PsExec (http://technet.microsoft.com/en-us/sysinternals/bb897553.aspx), but that's only good for a relatively small number of clients and if you're sure they're all running.

Thanks for the quick reply. How do I setup this script to install each .msp file?