Married in a civilian court but has not been wed in a Catholic ceremony, if I practice celibacy will I be eligible to receive communion? I am living with my wife and four kids.
Just a minor correction: Celibacy means not being married. You have entered into a civil marriage and therefore are not technically celibate. Because you are Catholic, it is an invalid marriage. To refrain from sexual activity in such a state is chastity not celibacy.
Your situation is a bit complicated. Marriage is a public act. Your civil marriage is a public action that is contrary to the laws of the Church. Therefore, even if you are living chastely you cannot receive communion because you are publicly living in contradiction to the laws of the Church. The remedy that is normative in such a situation is to have your marriage validated by the Church.
However, the Church does permit an occasional exception. You can apply to your bishop for permission “to live as brother and sister.” This would mean that the bishop has permitted you to receive communion if you and your wife commit to living chastely. Such permission is not easily granted, you’ll have to explain why having your marriage validated by the Church would be impossible or gravely inconvenient.