To disable strikethrough in a specific file, add the following to your file:
-*- org-emphasis-alist: (("*" bold) ("/" italic) ("_" underline) ("=" org-verbatim verbatim) ("~" org-code verbatim) ("+" (:strike-through nil))); -*-
The down-side is that it will complain that the file may contain values that are not safe (see here). You can also use the longer version at the bottom of your file, as mentioned here.
To do it for all your org files is a simpler, and will not ask questions:
(setq org-emphasis-alist (quote (("*" bold "<b>" "</b>")
("/" italic "<i>" "</i>")
("_" underline "<span style=\"text-decoration:underline;\">" "</span>")
("=" org-code "<code>" "</code>" verbatim)
("~" org-verbatim "<code>" "</code>" verbatim))))
Sources: Bernt Hansen's org-mode notes(a must-read) and the org manual