Here's what google translate came up with for the Hungarian part. Don't know that I can help with the Romanian(can't read the handwriting)

Oh, almighty, Lord, my God! I beg you, by the precious blood that flowed from the side of your divine Son Jesus, in the sight and greatest sorrow of his holy Mother: deliver the souls in purgatory, and especially the one who was most venerated by our Lady, that he may soon reach your glory, where he may be with you and you praise him forever. Amen.

Oh, almighty, Lord, my God! I beg you, by the precious blood that flowed from the side of your divine Son Jesus, in the sight and greatest sorrow of his holy Mother: deliver the souls in purgatory, and especially the one who was most venerated by our Lady, that he may soon reach your glory, where he may be with you and you praise him forever. Amen.

Artificial Intelligence says: The prayer you've provided is a variation of a prayer found in Catholic tradition, often associated with devotion to the Holy Souls in Purgatory. It reflects the Catholic belief that prayers and sacrifices can help souls undergoing purification in Purgatory to enter Heaven sooner.
Here is a breakdown of the prayer's meaning and components:
"Oh, almighty, Lord, my God! I beg you, by the precious blood that flowed from the side of your divine Son Jesus..." This part of the prayer invokes God's mercy by appealing to the sacrifice of Jesus, emphasizing the redemptive power of His blood.
"...in the sight and greatest sorrow of his holy Mother: deliver the souls in purgatory, and especially the one who was most venerated by our Lady..." This highlights the suffering of Mary, the Mother of Jesus, witnessing her Son's crucifixion. It also specifically asks for the release of souls in Purgatory, particularly those who were devoted to Mary.
"...that he may soon reach your glory, where he may be with you and you praise him forever. Amen." This expresses the ultimate hope for the deceased soul: to enter into God's presence and join in His eternal praise.
Significance in a Hungarian context:
Although this prayer is a general Catholic devotion, Hungarian funeral traditions often involve praying for the deceased, reflecting the country's Catholic heritage. Praying for souls in Purgatory is a common practice in Catholic funerals worldwide, as it is believed to help the deceased achieve full purification and enter heaven.
Note: Praying for souls in Purgatory has been a part of Christian tradition since the early Church, with support found in scripture and teachings about God's mercy and justice.