Do Jews believe that a person can sell his/her soul to the devil?
The idea of "selling one's soul to the devil"—meaning, becoming a slave of the devil in exchange for favors provided—does not exist in Torah. Jewish ethical works do describe instances where one can be somewhat "possessed" by evil drives. But even that state is always reversible.
Before addressing this, here's a bit on the nature of Satan in Jewish thought:
Satan is a Hebrew verb meaning "provoke" or "oppose" and is used several times in the Bible as a verb. The first instance is in the story of Balaam, when Balaam decides to take the mission of cursing the Jewish People:
"G‑d's wrath flared because he was going, and an angel of the L‑rd stationed himself on the road to oppose him [translation of l'satan lo], and he was riding on his she-donkey, and his two servants were with him.
In other cases, the word appears as a noun, "a provocateur." Generally, the title appears with the definite article—"the satan"—which means that it is not a proper name, just a job description. For example, in the book of Job, the satan appears as a prosecutor before G‑d:
"Now the day came about, and the angels of G‑d came to stand beside the L‑rd, and the satan, too, came among them…"
"Now the L‑rd said to the satan, "Have you paid attention to My servant Job? For there is none like him on earth, a sincere and upright man, G‑d-fearing and shunning evil."
And the satan answered the L‑rd and said, "Does Job fear G‑d for nothing? Haven't You made a hedge around him, his household, and all that he has on all sides? You have blessed the work of his hands, and his livestock has spread out in the land. But now, stretch forth Your hand and touch all that he has, will he not blaspheme You to Your face?"
Now the L‑rd said to the satan, "Behold, all that he has is in your hands; only upon him do not stretch forth your hand." Now the satan left the presence of the L‑rd."
From this passage, we see that G‑d created an angel to play the role of provocateur; that he is a messenger of, and subservient to, G‑d. He was not a fallen angel or sent to Hell, where he began fighting G‑d; he was created to be Satan. Neither does Satan spend his days stoking the flames of hell with his pitchfork. He is a presence on earth with a mission: to provoke people to disobey G‑d's will.
Indeed, the dualistic notion of a powerful anti-G‑d figure that fights with G‑d for the destiny of the human race is incompatible with Jewish belief. There is no power of evil independent of G‑d; otherwise this would imply a lack of G‑d's all-inclusive control and power. To quote the Book of Isaiah:
"…from the place where the sun rises until the place where it sets, there is nothing but Me. I am G‑d, there is nothing else. [I am He] Who forms light and creates darkness, Who makes peace and creates evil; I am G‑d Who makes all these."
Obviously then, the satan is not an autonomous force who opposes G‑d and recruits people to his militia. Rather, the satan is a spiritual entity that is completely faithful to its maker. For example, regarding the Biblical story of the satan's particularly aggressive attempt to seduce Job to blaspheme, Rabbi Levi declares in the Talmud:
"Satan's acted for G‑d's sake. When He saw how G‑d was so focused on Job, he said, "Heaven forbid that G‑d should forget His love of (our forefather) Abraham!""
The Zohar compares the satan to a harlot who is hired by a king to try to seduce his son, because the king wants to test his son's morality and worthiness. Both the king and the harlot (who is devoted to the king) truly want the son to stand firm and reject the harlot's advances. Similarly, the satan is just another one of the many spiritual messengers (angels) that G‑d sends to accomplish His purpose in the creation of man.
This is not the satan's entire job description. The Talmud sums it up saying that the satan, the impulse to evil ("yetzer ha-ra"), and the angel of death are one and the same personality. He descends from heaven and leads astray, then ascends and brings accusations against humankind, and then carries out the verdict.
However, the above-mentioned passage in Zohar concludes that if one does succumb to the urging of the evil inclination, he is "giving energy to the other side". This means, that an act defying G‑d's will grants those forces that hide G‑d's presence—at His bidding—additional strength to hide G‑d from us even more. This presents itself as even greater internal and external challenges for one to experience and identify with the truths of G‑d and His Torah.
One extreme example of this would be Pharaoh, who enslaved the Jewish people in Egypt. Though G‑d told Moses to command Pharaoh to free the Israelites, He stated that, "I have hardened his heart and the heart of his servants" in order to ultimately punish the Egyptians with the ten plagues. As a consequence for his earlier oppression and abuse of the Jewish nation, his ability to abandon his evil ways was made even more difficult, to the point that he seemed to have lost free choice, and his vision and ability to repent was completely impaired.
There is nothing that can ultimately stop one who truly seeks to return. Pharaoh, too, was therefore still capable of overcoming this block, and ultimately repenting, as discussed at length in Why was Pharaoh Punished? Thus, even when someone seems to be completely possessed by the satan–as divine retribution for his earlier misdeeds, not by choice of negotiation with the devil—he is still not sold, and can overcome his instinct and impulse to act satanically. To become completely sold with no hope of redemption would be counter-productive of G‑d's intent, and could not exist.
Regardless of where you've fallen, you are never sold to these impure forces, and your soul can wrestle free and recommit to serve G‑d with sincerity and passion. The axe of earnest remorse can bring down any wall, whether preexisting or created by your actions, clearing the way for you to come home to your true self.