You find both accusative pronouns (me/him/her/them) and nominative pronouns (I/he/she/they) in this syntactic position in standard English. The forms with the nominal genitive pronouns (mine/yours/hers etc.) are a red herring because they stand for something possessed rather than the person themself.
The traditional rule for comparison with a person is that you must use nominative. However, according to my research, accusative is more common.
I searched the Corpus of Contemporary American English for this syntactic structure, followed by a comma or a period to ensure we are not looking for cases like faster than he is, with a verb following the pronoun, in which case nominative is obligatory.
There were 1046 results for the accusative pronouns and 450 for nominative pronouns, more than 2 to 1 in favor of accusative pronouns—the “traditionally wrong” form. Both forms are standard, so my advice to a writer choosing between these forms is to consider that the “traditionally correct” form is unimpeachably correct but a bit formal. Choose the form that best matches tone and formality level of your writing.
For the curious, the queries looked like this:
[jjr*] than me|him|her|us|them .|,
[jjr*] than I|he|she|we|they .|,
where[jjr*]
means any comparative adjective.
Update 2011-05-23
Using the new Google Book Corpus search, I was able to construct a Google ngrams-like graph comparing these usages over time, using these two queries: accusative, nominative:
As you can see, until the late 1980s, the formal usage was more common than the informal usage. Since then, however, accusative has very rapidly eclipsed nominative, even in this corpus, which represents professionally published works.
(1) and (3) are equally grammatical, but (2) is ungrammatical. Order is a ditransitive verb, which means it can be followed by an indirect and a direct object as in (1), but it is possible to replace the direct object with a prepositional phrase, as in (3).
Best Answer
Saying "I ordered it offline" might lead me to ask "So, did you order it by phone, or in person?" It would not imply the same as "I ordered it online."
Saying "I ordered it off the internet" means (to about 99% of US English speakers) the same thing as "I ordered it online."