His company has an annual dinner that they call the Christmas dinner
Praise be to Allah.
It is not permissible for a Muslim to participate in the religious festivals of the disbelievers in any way whatsoever. Doing that is a grave major sin, because by doing that he is helping and encouraging others to ascribe partners to Allah, may He be exalted, and he is expressing approval of that.
Hence it is not permissible for the Muslim to congratulate the disbeliever on the occasion of these festivals or to give him a gift on such occasions. This has been explained previously in the answer to question no. 947.
This celebration (the annual dinner) mentioned in the question is given, by the people who organise it, the name of their religious festival (Christmas). The period for Christmas celebrations, among them, is not just one day; rather it is a number of days beginning on Christmas Eve (December 24) until January 6, i.e., thirteen days.
One of the rituals that are observed on this day by them is eating a dinner which they call “Christmas dinner”, and exchanging gifts. This is what is mentioned in the question that they will do at this celebration, which makes it more likely that it should be described as a religious celebration or, at least, a kind of customary celebration for a religious reason, or connected to that. This is what makes it disallowed for the Muslim to participate in it or to congratulate those who are celebrating it.
If it is the usual practice for the employees of the company to take part in this dinner, or if you are invited to it directly, then try to give whatever excuse you can and use whatever tricks you can to avoid it. In fact we have seen that many respectable companies respect the religious sentiments of their employees, so if you explain that you have a religious excuse that prevents you from participating in this celebration, then respectable companies such as this will understand that and will respect the employee’s feelings.
For more information, please see the answer to questions no. 127500 and 85108.
May Allah, may He be exalted, help you to do that which He loves and which pleases Him.
And Allah knows best.