How do "power of God" in 1.16, "righteousness of God" in 1.17, and "wrath of God" in 1.18 all relate? All have the same structure in Greek. The gospel is the key here. Power is unto salvation through the gospel. In the the gospel, the righteousness of God is revelaed. So, does wrath come upon those who have no power or righteousness through the gospel? I believe so. Those recipients of the wrath of God in 1.18 have stiff-armed the "truth of God" in 1.18 and 1.25. The immediate need here is righteousnes [or a righteouesness] because the wrath of God comes upon all unrighteousness in 1.18. The gospel grants power unto this end.
Pardon my Pauline keyboard-brainstorming. See the gospel in Isaiah 52.7 and Nahum 1.15.