In regards to celebrating or observing Hanukkah and other non-Christian feasts/celebrations, I think it depends how they are observed. For example, if I were a Jew and I celebrated Christmas, I could (a) celebrate it in a small way, such as getting together with family on Christmas day and having dinner, (b) give people gifts and accept gifts from others, and I could have lights on the outside of my house and maybe even have a Christmas tree, or (c) celebrate Jesus' birth as well as the secular Christmas (or even instead of) setting up a crèche in my home and possibly even going to church.
If the same degrees of celebration were applied to other religious festivals/feasts/fasts, then (a) would probably be okay in most instances (for instance I could fast during Ramadan, but not with the same intentions as a Muslim would, rather I would fast with the same disposition as I would during Lent, and thus would not truly be observing the Ramadan fast), (b) would depend on the feast, but in many cases would probably be a venial (minor) sin, while (c) would be a venial sin at the least, depending once again on the festival and the celebrations involved, but fully engaging in the celebrations could quite likely be a mortal (serious) sin. The degree of seriousness for (b) and (c) would likely depend on the religion (for instance, I could celebrate the feast day of an Orthodox saint, which might not even be an offense at all and a Jewish festival that involved worship would be to the same god and would thus not be as big a deal as some cult festival that involved human sacrifice--to use an extreme example to demonstrate my point). It would also depend on the character of the celebrations and the disposition of the person celebrating. With the degree of celebration in (a), a venial sin could be committed, once again depending on the celebration.
In regards to Hanukkah specifically, (a) would not be a sin, (b) would be a venial sin, depending on the knowledge and disposition of the person involved, and (c) would be a more serious venial sin, once again depending on the person's knowledge and disposition. In this particular instance, it would only be a mortal sin if the person involved believed it was seriously wrong and celebrated it anyway.