Unfortunately, you may not be able to. However, let’s break it down, since there are different types of “irregular unions”.
Is it a civil wedding? Many immigrants may come from nations that, due to a history of anti-clericalism, require civil ceremonies. So, if the couple does not have other impediments, then it would be a simple matter of convalidation. BOOM! DONE!
If it is a matter of cohabitation, and they have no other impediments, pastors can “highly encourage” them to marry. BOOM! DONE!
If it is a case of divorce/remarriage, “highly encourage” the divorced party/parties to apply for an annulment.
However, at some point, either while waiting for the regularization, or if it cannot be regularized, someone will have to break the news that either they will have to live like brother/sister or break up or refrain from Eucharist. In the case of divorced people, one can simply state that this comes from Jesus Himself, and they can’t escape by running off to a “Bible church” because that is in their bibles, too. This is also true of a same-sex situation.
How to reach out to them? Well, they may reach out to the Church if they want sacraments for their children; that could serve as an evangelization moment where they can be “encouraged” to regularize their situation (the priest could do so be simply but gently explaining that he is concerned about the home life of the child being a danger to the faith).