Is a crucifix important during exorcism?

Answer 1

It can be, but it is not essential. Demons are exorcised from those possessed by the power of Our Blessed Lord, through His minister, the priest. This is done through prayer. Different sacramentals may be used during the ritual, but they are not necessary to the ritual itself. What is necessary is the ordained priest, and his faith in Our Blessed Lord. The most important things for a complete exorcism are the sacraments, as these are the grace of Our Blessed Lord, and, in the case of the Most Holy Eucharist, Our Blessed Lord, Himself. For a complete discussion of exorcism, please read Fr. Gabriele Amorth's book, An Exorcist Tells His Story. Fr. Amorth is currently the chief exorcist for the diocese of Rome - he is the Holy Father's Exorcist.

Answer 2

An exorcism is a ritual nominally intended to remove demons from those unfortunate enough to be possessed by demons. It is full of symbolism and, in the Catholic Church, there is no more powerful symbol than the crucifix. They are a medieval ritual intended to impress the faithful with the power of the Church, and this is why symbolism is important. But it is not only the crucifix that must be present during the ritual of exorcism, but a relic of a saint, with a 'first class relic' to be preferred.

If demons are real, then presumably they could be exorcised merely by prayer, perhaps even in the absence of a priest, but demons are not real. Although exorcisms do not really remove demons, it is the symbolism that is important, so therefore the crucifix is important, as is the relic.