Is it obligatory to attend a condolence gathering, or is offering condolences over the phone sufficient?

Consoling the family of the deceased is recommended, not obligatory. The Prophet, peace and blessings be upon him, encouraged it through his words and actions. Allah Almighty promised that whoever consoles his brother in misfortune, Allah will clothe him with garments of honor on the Day of Resurrection. It is not a condition to go in person to the afflicted; a phone conversation or similar means suffices, according to custom. Consolation may become obligatory if the one being consoled is a relative with whom ties of kinship must be maintained. Neglecting it then is considered a forbidden severance of ties. In such a case, the method of offering consolation reverts to custom: if custom dictates a personal visit, then a visit is obligatory unless there is hardship; and if custom dictates that a phone call suffices, then there is no objection to that.