There isn't any reason why Dr. Strange would be able to use Thor's hammer, the kind of person with the mindset to call upon the power of Mjolnir is very limited and to date all those we've seen gain its powers even briefly were men of action and selfless in the extreme and given the chance to be warriors as the Asgardians are. Captain America, Eric Masterson, Dargo, Rogue (Alternate Timeline), Beta Ray Bill, all were selfless warriors when the time came and the hammer responded.
The only one to ever use the hammer who was unworthy was Red Norvell and that required his acquiring a template of Thor's power Odin kept around along with Thor's Belt of Power and Iron Gloves, the only things that will let one unworthy carry (but not use) Mjolnir. While he later got full Thor status and his own copy of Mjolnir I don't believe he'd be worthy of lifting the original even now although it's always possible he's grown into that kind of worthiness.
I can't think of many Marvel characters that might end up worthy, perhaps the Illuminator (short-lived teen character with light-based powers and an attempt at a Christian hero that failed), Spider-man if he weren't weighed down by his guilt over his Uncle, and maybe Daredevil (who's certainly a brave warrior who managed to survive in Mephisto's hell and all its torments, to even light a clean spiritual fire in the place later used by another hero to escape).
"A shared universe, like any fictional construct, hinges on suspension of disbelief. When continuity is tossed away, it tatters the construct. Undermines it."
-- Peter David
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