Single quotes in string with jQuery ajax

Javascript has a built in method just for this that covers more than just single quotes. Its called encodeURIComponent, from Javascript Kit:

Used to encode the parameter portion of a URI for characters that have special meaning, to separate them from reserved characters such as "&" that act as key/value separators. More inclusive than encodeURI(), it encodes all characters with special meaning in a URL string, including "=" and "&". Use this method only on the parameter portion of a URI; otherwise, the URI may no longer be valid if it contains one of the characters that are part of a valid URI (ie: "+") yet should be escaped if part of the URI parameter.

So your code should become:

data: "{str_" + encodeURIComponent(sectionName) + " :'" + encodeURIComponent(UpdateText) + "',EntityID: '" + encodeURIComponent(EntityID) + "' }",

I encode everything I send in a query string to be safe, but encoding the EntityID could arguably be skipped because it doesn't come from the user(I'm assuming), so you know it won't have special characters.