Example: If a Flip Effect activates after "Ehren, Lightsworn Monk" returns the Flip Effect monster to the Deck, then "Divine Wrath" may be Chained to the Flip Effect. The Flip Effect will be negated, but the Flip Effect monster will not be destroyed and will remain in the Deck.
Freed the Matchless General: The effect of "Freed the Matchless General" can only be activated when you draw during your Draw Phase. Suppose you control two copies of "Freed the Matchless General". If you activate the effect of one copy, then you cannot activate the effect of the second copy in a new Chain after the first one resolves, since the activation timing is no longer correct. Thus, if you activate the effect of one copy and its activation and effect are negated by "Divine Wrath", then you cannot activate the effect of the second copy after "Divine Wrath" resolves, since the activation timing is no longer correct.
During the Damage Step, in general, you cannot activate Spell/Trap Cards other than Counter Trap Cards and ATK/DEF-increasing/decreasing effects. Thus, you cannot activate "Book of Moon" nor "Raigeki Break", but you can activate the Counter Trap "Divine Wrath" during the Damage Step.
Previously Official Rulings
These TCG rulings were issued by Upper Deck Entertainment and have since been deemed unofficial by Konami. They were previously considered official and can still be correct, as long as they follow the official gameplay rules, or unless Konami has issued a ruling that says otherwise. References: 
If you activate "Divine Wrath" during the Damage Step to destroy the attacking monster or the monster being attacked, the monster is destroyed. No replay occurs because a replay can only happen during the Battle Step. If damage calculation has not been performed yet, it is not performed.
You can activate "Divine Wrath" when "Vampire Lord" or "Sacred Phoenix of Nephthys" activate their effects in the Graveyard, and their effects are negated and they are not Special Summoned; but because they cannot be "destroyed" while in the Graveyard, they are not destroyed by a card effect so their effect will not activate again.
You can activate "Divine Wrath" when a "LV" monster is sent to the Graveyard to Special Summon the next level version (an Ignition Effect)[Notes 5], and "Divine Wrath" will negate that effect, even though it cannot destroy the "LV" monster because it is already in the Graveyard.
↑Konami Judge Program Rulings are considered unverified, as their source(s) are not publicly viewable. They are not confirmed as applicable to the TCG until they have been officially published by Konami.
↑The latest print of "Helpoemer" has Problem-Solving Card Text which states that its effect only requires it to be in the Graveyard due to being destroyed by battle, so its effect can be activated again even if its effect is negated by "Divine Wrath".
↑The latest print of "Sinister Serpent" has Problem-Solving Card Text that states that its effect can only be used once per turn, so even if its effect is negated it cannot be activated again during that same turn. This difference is due to a major change in the functionality of "Sinister Serpent".
↑Konami FAQ: Does the effect which removes from play "Dark Magician of Chaos" begin a chain (for "Divine Wrath")?
↑ 6.06.1Konami FAQ: If "Shadow-Imprisoning Mirror" is active and "Ehren, Lightsworn Monk" attacks a Flip Effect monster, then is the Flip Effect negated?
↑Konami FAQ: When the effect of "Elemental HERO Absolute Zero" activates in the Extra Deck, can "Divine Wrath" be activated?
↑Konami OCG FAQ: Can "Divine Wrath" (etc) be activated when "Exodia the Forbidden One" (etc) are in the hand?
↑Konami FAQ: If you control two copies of "Freed the Matchless General" and "Divine Wrath" negates the activation of the effect of one copy, then can the effect of the other "Freed the Matchless General" be activated?
↑Konami FAQ: When the effect of "Majestic Star Dragon" which negates the effects of an Effect Monster activates, does it start a Chain Link?
↑Konami FAQ: Can the effect of "Stardust Dragon" be activated in Chain to the activation of a Counter Trap Card?
↑Konami FAQ: When "Stardust Dragon/Assault Mode" does not negate the activation of the effect of a card, can it Special Summon itself during the End Phase?
↑Konami FAQ: Can "Divine Wrath" be activated if "Sun Dragon Inti" is in the Extra Deck?
↑ 14.014.1Konami FAQ: Can "Sword Master" be Special Summoned if the attacked monster is destroyed by an effect after damage calculation?
↑ 15.015.1Konami FAQ: The effect of "The Fabled Unicore" can negate an opponent's card if the hand sizes are the same at what time?
↑Konami OCG FAQ: Can you activate Quick-Play Spell Cards, Counter Trap Cards, and so on during the Damage Step?