How does the Orthodox Church interpret Romans 5:9 when it states our Lord's blood justifies us and therefore we will be saved from wrath?
I can't speak for my whole Church, but I'd say that because Christ fulfills the need for a righteous man to fill up the iniquities of Israel, the wrath against Israel produced by his [Israel's] estrangement from God is removed. It is this condescension, to enter into Israel as the righteous Man, and to follow him into Death by becoming sin, though sinless, so that the Righteous Man could fill up even death with Himself, that accomplishes the expiation of mankind. The debt is a debt of *righteousness*, not of a need for a suitable punishment victim.
For this reason it was said:
"Therefore will I divide him a portion with the great, and he shall divide the spoil with the strong; because he hath poured out his soul unto death: and he was numbered with the transgressors; and he bare the sin of many, and made intercession for the transgressors."
To which Paul contributes: "For as much then as the children are partakers of flesh and blood, he also himself likewise took part of the same; that through death he might destroy him that had the power of death, that is, the devil..."
"All we like sheep have gone astray; we have turned every one to his own way; and the LORD has laid on him the iniquity of us all."
"The Spirit of the Lord YHWH is upon me; because YHWH hath anointed me to preach good tidings unto the meek; he hath sent me to bind up the broken-hearted, to proclaim liberty to the captives, and the opening of the prison to them that are bound".
Really depends on whose legal system we're talking about here. Read the Epistle to the Hebrews for that.
but wouldn't the Orthodox agree that Christ delivers us from wrath by giving us new life?
We would agree.