Is expiation (kaffarah) obligatory for one who swore by Allah Almighty not to look at forbidden images on the Internet, then searched for information on the hymen out of scientific curiosity to alleviate obsessions, and in the same context, out of scientific curiosity, came across scientific images of the male 'awrah (private parts) on the same website?

The fundamental principle concerning oaths is the intention and purpose of the one swearing the oath. If your intention was never to access any websites whatsoever, then you have broken your oath and expiation is required. However, if your intention was not to access them out of lustful desire, then there is no breaking of the oath and no expiation. If you had no specific intention, then the oath relates to the reason that prompted you to make it. One should be wary of the whispers and deceptions of Satan, and seek assistance from Allah, engaging frequently in remembrance of Him and prayer.