How does the Catholic Church explain going to the sacraments in similar situations?
Each person’s return to the practice of the Catholic Faith is unique and does not have to be done alone. One should strive to seek the spiritual light of a good and theological solid minded priest in each individual’s particular case.
There at times, seems to be a myriad of different variables that make this one of those questions almost impossible to have a standard response.
For this reason many priests will have to have recourse to the local canon lawyer of the diocese and/or the diocesan marriage tribunal in order to determine if one or any of your previous marriages were valid.
Although you state that you were married three times, you have not mentioned if your spouses died before you were remarried. These facts must be taken into account.
If you were married between 1983 and 2006, a loophole existed for some mixed marriages to possibly be seen as valid in the Catholic Church.
Marriages of non-Catholic Christians (Protestant marriages)
Baptized Protestants are not bound by the form of marriage, i.e., they do not have to exchange their consent in the presence of a Catholic official. A baptized Catholic who left the church by a formal act and married after the year 1983 (the year the present code of law went into effect) is not bound by the form of marriage either.*
*The motu proprio Omnium in mentem of 26 October 2009 has now been altered, by Pope Benedict XVI and formal acts of defection from the Catholic Church are no longer recognized by the Church. ”After 4 decades” of not being within the fold puts you in this time frame, so you need to truly seek information from diocesan authorities as how to continue. Nevertheless, be courageous, the Church is there to help you on you journey back.
For the rest, one can follow the general counsels given in Geremia’s answer, although I would prefer a more reconciliatory tone, in his response.