Is there a Jewish equivalent to Christian's upside-down cross, a symbol that some Christians believe to mean "evil" or the "devil."
Does the "average" Jew have a visual symbol which might be taken to mean evil or the devil?
Welcome to Mi Yodeya, Frederick.
The "average" Jew does not have a symbol for "evil" or the "devil," especially the latter. The "devil" is a Christian innovation shared also by Islam, and which probably owes some of its origins from pagan and other non-Christian sources such as Zoroastrianism and Manichaeism, both of which are dualistic religions. Moreover, the Christian visage of the Devil has evolved greatly over the centuries. Since this site is about Judaism and not about Christianity, I will refer you to Wikipedia as my source for that info.
Judaism does not recognize the personage of "the Devil" and it understands the angel Satan in a much different way than Christians understand him. The Hebrew Scriptures do not make much reference to Satan. He appears principally in the Book of Job. At Job 1:6 the verse refers us to a group of angels it calls the "sons of G-d" or in Hebrew, "b'nai HaElokim." When the Hebrew Scriptures use the word "Elokim" [note that I am intentionally misspelling it as it is a Name of G-d], it refers to G-d when His attribute of justice-seeking is most prominent. Therefore the "b'nai Elokim" are those angels who serve that particular attribute. The verse describes Satan as one of those angels. There and the subsequent paragraphs Satan is clearly working for G-d, acting here as an accusor of Job, which is appropriate as the word "satan" means "adversary." Throughout the Book of Job, the Satan clearly takes his orders from G-d. Judaism does not have a concept of fallen angels or one that is as out-of-control as the Christian Satan seems to be. To accept that concept, one would have to reject the concepts that G-d is the only god (Deut. 6:4; Isa. 45:5) and the concepts that G-d gave us the inclination to do good and the inclilnation to do evil when He gave us Free Will. Deut. 30:15-20. It is from other religions that Christianity got the idea that Good and Evil are at constant war and G-d is on the side of Good, and the Devil is on the side of Bad. To accept that idea, we would also have to believe that G-d doesn't win every battle.
G-d created good and evil, as He did all things. Isa. 45:7. He had to when He gave us free will, otherwise we would be sock puppets in a play not of our own choosing. The evil and good that we choose are relative. The ultimate good that G-d creates is Choice, i.e. Free Will, and our ultimately capability to overcome our evil inclination.
There may have been, from time to time, images that were understood to be inherently evil to Jews, the Swastica for one, but they were not our images in the first place and are merely images we associate with the evil done to us.