First, regarding Abraham. Note that it would not be the righteousness of Abraham that could potentially secure the saving of all the inhabitants in the Sodom and Gomorrah region. That would require finding 10 righteous men who inhabited the towns. Abraham pleaded on their behalf, but not on the basis of his own good standing before God.
Alas, God could not find even 10 righteous men in the whole region. There was only Lot (who was called 'righteous' later on in the New Testament - 2 Peter 2:7) so Lot had to flee for his life, and that of his family. So much for faithful Abraham's plea, "Will you sweep away the righteous with the unrighteous?" (Gen. 18:23) The only righteous person had to be dragged out by angels, at the last gasp, because there were only unrighteous people all around.
Abraham could only plead on the basis of God being the righteous judge of all the earth (vs.25), and it became clear that God's judgment of Sodom and Gomorrah was entirely righteous, because only one righteous man was there, who was rescued from the wicked unrighteousness all around him.
Second, regarding Ezekiel. The build-up to God's judgment of that nation is detailed in the preceding verses. All their princes were evil, the prophets were lying, all the people were unholy, profaning God, murdering for unjust gain, oppressing the poor, ill-treating the alien residents and denying them justice. Ch.13 details no-one "building up the wall" or, standing in the breach, therefore God gave ample warning through faithful Ezekiel that the violent thunder-storm of his judgment would suddenly break. How that resonates with Revelation's warnings, and the judgmental plagues God pours on an increasingly godless world after Christ's ascension!
Third, regarding Noah who found grace (favour) with God due to his faith. Note how the only other righteous man mentioned was Enoch, but God had taken him away. That meant that in Noah's day, "Every inclination of the thoughts of [man's] heart was only evil all the time" (Gen. 6:5). They were given ample warning of God's coming judgment but they scoffed and ignored it, continuing in their godlessness. "They took no note until the flood came, and swept them all away" Jesus said, adding that it would be just the same prior to him returning suddenly to bring in the Day of Judgment (Matthew 24:37-44).
Also note how Noah, a preacher of righteousness (Heb.11:5-7) condemned the world (as did Ezekiel re. the nation of Israel). God is righteous and sends his servants to warn of his coming wrath so that nobody will be able to claim they didn't know. Even before Jesus spectacularly returns there will be angelic warning of the beginning of the gospel, to the whole world, to fear God and worship him, and to repent of their evil (Rev. 14:6-7) but they won't. Only what Christ did can save anyone; the righteousness of God was publicly displayed at Golgotha and the empty tomb, but nobody at the time saw it like that.
There's no excuse now, for God's word has explained the full gospel. All those who will be judged by Christ will not be able to say that they weren't warned - just as at the time of the Flood - and only the righteousness of God, through Christ, is the righteousness that saves any individual in any generation.