If you are not Thor, but are worthy and hold his hammer, Mjolnir, then you shall wield the power of Thor.
But if you are Thor, and are worthy, but do not hold Mjolnir, then do you still possess the power of Thor?
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This is a complex topic because the power of Thor came in a variety of flavors depending on when you meet the God of Thunder:
Thor has a number of superhuman abilities which take place no matter whether he uses Mjolnir or not. His strength is greater than the average Asgardian due to his relationship with his mother, the Earth Goddess, Jord/Gaia. His strength is effectively limitless but has been measured as at least 100+ tons.
His Asgardian tissues are three times as dense as a normal Human. He is more durable and resilient than a normal human due to his enhanced molecular density. He is, especially when wearing enchanted Asgardian armor, resistant to normal Human weapons.
While Thor was growing up, he did not have Mjolnir. He simply had his great strength and was a capable warrior of Asgard. His hundreds of years of experience in combat are part and parcel to his fighting abilities and he is more than a capable combatant even without Mjolnir.
In Thor's youth he was strong and tough and fought against the enemies of Asgard with sword and shield. Later when Odin wanted Thor to take on more responsibility, he gave him the warhammer, Mjolnir. In the Marvel universe, Mjolnir was a gift that Odin reserved the right to revoke its capabilities to Thor as HE saw fit.
When Thor was deemed arrogant and unworthy, Odin took Mjolnir and the physical capabilities of Thor away from him and merged him with a mortal doctor, Doctor Donald Blake. This was part of an enchantment he cast upon Thor. By being the partially lame, Dr. Blake, Odin hoped Thor would learn humility and to love Midgard as a place to be protected.
When Doctor Blake found Mjolnir disguised as a staff, he would strike it upon the ground and become the Mighty Thor. The power of Thor was literally bound up with the hammer making an ordinary mortal, Thor. But Thor was not always aware of his complete heritage. The hammer also had a limitation that if Thor did not make contact with the hammer for 60 seconds, he would revert back to Donald Blake.
Thus the nature of the writing upon the hammer which implied that the power of Thor was completely held within the hammer. But technically, the power of Thor is two-fold. One part was an enchantment which released Thor's abilities to THOR who was depowered by Odin as a part of a punishment.
The Power of Thor is partially the ability to manipulate the energies, magic and capabilities of Mjolnir. But if Thor is lending the hammer to someone else (Superman for example) Thor doesn't lose his powers, or become enfeebled as he might have done once upon a time when Mjolnir had an enchantment where if Thor did not come into contact with the hammer in 60 seconds, it reverted back to a staff.
The second power of Thor is the ability to command Mjolnir such as Jane Foster does when she uses the Mjolnir in her guise as Thor. Since she is using the hammer at the moment, she is stronger, faster, more capable than she ever would be as a Human, so she is experiencing the Power of Thor as more than just a command of the hammer, but as an improvement of her physical abilities giving her a degree of superhuman strength, speed and resilience.
Thor Odinson, who currently isn't wielding Mjolnir, is no longer under a limiting enchantment, so he is able to retain his incredible strength, resilience and durability that is his as a son of Odin and Jord. He makes use of a mighty axe, Jarnbjorn and has a nigh-invulnerable metallic arm made of Uru.
There have been more than one instance where Thor is unable to reach his hammer, needed the help of another hero (Steve Rogers, as the Captain) who was able to partake of the power of Thor, particularly superhuman strength, while NOT taking away any of Thor's abilities from him during this temporary transfer of power.
As shown in this image of the Captain (Steve Rogers) using Mjolnir, he is using it because Thor is under duress. They are battling Grog and the Demons of Death. Thor is unable to summon Mjolnir to him. The Captain decides he should try and return Mjolnir to Thor, but knows normally no one can lift it. But he decides he has to try. [From Thor #390, 1988]
In this moment of extreme crisis, the Captain "levels up" in the worthiness quotient because Thor is unable to help himself and only with help will he be able to fight his way free. Steve Rogers IS worthy, but it is because in this instance he sacrifices himself as a warrior should, does he become warrior enough, and worthy enough, to wield Mjolnir and its power for even a moment. He does the right thing immediately after that and throws Mjolnir to its rightful owner.
For the record, Steve Rogers will wield the power of Thor during the 'Fear Itself' saga, but again Thor is "in extremis" and the Captain is wielding the hammer in order to bring the battle to the enemy and return the hammer to Thor. In both cases, Thor is temporarily incapacitated.
The current answer is from a comics perspective but this is tagged with the MCU tag and as of Thor: Ragnarok we have an explicit answer for this. In short yes you will still have the power of Thor. We see this a few times in the film, first when Thor and Hulk are fighting on Sakaar. But the best moment is probably the final fight montage on the Rainbow Bridge. It is worth noting that at this moment in time Mjolnir is destroyed.
And of course Odin even states as such that Mjolnir was only there to help Thor focus his powers.
Odin: Are you Thor, God of Hammers? That hammer helped you control your power, focus it. But it was never the source of your strength.
The Answer is: Of Course, YES Thor, as the god of thunder, isn't dependent on his mighty hammer - Mjölnir. Thor has bunch of powers duo to Mjölnir, but he can still control weather, manipulate lightning and etc. Jason Aaron's Unworthy Thor run showed Thor can still do it. In his fellow times, when he didn't have mjolnir, he was still able to use his godly powers. For further information, you can read "The Unworthy Thor" comic. I know he is Unworthy there; but I don't think that'd make a difference.