Flying is an evasion ability. These abilities limit which creatures can block the attacking one. An attacker with Flying can be blocked only by a creature with either Flying or Reach. A creature with Flying can block non-Flying ones (if there is no effect stating the opposite: Skywinder Drake).
If a Flying ability was given or lost after the blockers were declared, the creature remains blocked or unblocked as it was. Flying doesn’t change the damage assignment in any way. It only defines if a creature can be declared as a blocker during the declare blockers step. For example, a token created by Flash Foliage can block a creature with Flying because it was never declared as a blocker. It appears on the battlefield already as a blocker.
If a creature gets several instances of Flying, it doesn’t matter, as “extra” Flying is ignored.
The second ability is much more interesting. Angelic Overseer always has it (if there are no effects that may influence the ability’s existence). It works when Angelic Overseer is on the battlefield.
Angelic Overseer has Hexproof and Indestructible only if you control a Human. If you don’t control a Human, or a permanent that you control ceased to be a Human, Angelic Overseer’s second ability doesn’t do anything.
An effect defining the subtype rewrites all the subtypes existing before*. When affected by Turn to Frog your Human stops being a Human and becomes a Frog.
If a cunning opponent snatched your only Human from you with Olivia Voldaren’s help, you’re in trouble. You don’t control a Human anymore, despite it still being on the battlefield.
Gideon Jura animated by his third ability has a Human subtype. This effect ends on the cleanup step, the aforementioned Planeswalker stops being a creature, and thus, a Human.
We now will assume that in every situation we control Angelic Overseer and a permanent with a Human subtype. If something happens with the Human, it is indicated explicitly.
Hexproof means that Angelic Overseer can’t be a target of spells and abilities your opponent controls. In contrast to Shroud, you (or your teammate in 2HG) can target a Hexproof creature. It’s pretty convenient: you can enchant, equip and give Angelic Overseer other different perks, turning it into a nearly invincible killing machine, as your opponent has almost no ways of dealing with your Angel.
Your opponent can’t target your Angelic Overseer with any of these spells.
The opponent can’t cast Arrest targeting Angelic Overseer.
However, your opponent can enchant your Angelic Overseer with an Arrest that was returned when Sun Titan’s trigger resolved. Learn more.
Your cunning opponent can target Angelic Overseer with your own spell, for example, by using Redirect.
Hexproof doesn’t save from spells and abilities that have no target:
Black Sun’s Zenith doesn’t target. Its effect puts counters on every creature (that can have counters placed on it).
Proliferate means choosing any number of players and/or permanents. If Angelic Overseer has counters, you can increment their number.
Phyrexian Metamorph doesn’t have the word “target” in its text. Thus, your enemy can copy your Angelic Overseer.
Both Hexproof and Shroud work only when the object with this ability is on the battlefield.
These abilities don’t work in other zones, that’s why spells with Hexproof or Shroud can be canceled.
Indestructible is a static ability. You could notice that cards printed before Magic 2014 have “is indestructible” in their text. Now cards have “Indestructible” or “has/gains indestructible” printed on them.
A permanent can gain or lose Indestructible via effects that give or take abilities. If the effects are independent, they are applied on the same layer, and the one with the newest timestamp overwrites the other.
If you control Angelic Overseer and Humility enters the battlefield, Angelic Overseer loses all abilities including Indestructible. It doesn’t matter if you controlled a Human before or after Humility has appeared. Angelic Overseer’s ability has the timestamp that appeared with Angelic Overseer entering the battlefield. Humility’s effect will overwrite Angelic Overseer’s abilities.
If you enchant a creature with Indestructibility after Humility has entered the battlefield, this creature has Indestructible because Indestructibility’s timestamp is newer than that of Humility.
If an effect states that a creature loses all its abilities, it doesn’t matter how the abilities got there in the first place. When you cast a Fused Turn//Burn targeting Tajic, Blade of the Legion, he loses all abilities and becomes a 0/1 Weird with two damage marked on him. And thus Tajic, Blade of the Legion will be destroyed, as he was dealt lethal damage.
Exactly the same happens if a creature gains Indestructible as Withstand Death resolves and then gets a Fused Turn//Burn – it is destroyed.
As Indestructible wasn’t an ability before M14, removing abilities did not remove indestructibility that was granted by an external effect (like Withstand Death). Those who are interested in non-ability effects can study things like “can’t be blocked”.
A permanent with Indestructible cannot be destroyed.
This means that effects which instruct you to destroy this permanent don’t work. However, nobody can forbid you to create such effects. It’s absolutely legal to target Tajic, Blade of the Legion with Liturgy of Blood. Despite the fact that Tajic will remain on the battlefield you will get mana.
A permanent with Indestructible can’t be destroyed as SBA are performed (those of lethal damage and damage from a source with Deathtouch).
Angelic Overseer will survive when damaged by Lord of Lineage, as SBA instruct us to destroy the creature that has been dealt lethal damage. Indestructible prevents this.
Angelic Overseer will also survive a skirmish with Acidic Slime. SBA instruct us to destroy the creature that has been dealt nonzero damage from a source with Deathtouch.
Day of Judgment destroys all creatures. However, when its effect is applied, you still control a Human, and so Angelic Overseer is Indestructible. This Human is destroyed and Angelic Overseer is not.
Indestructible doesn’t mean that there’re no ways to deal with the indestructible permanent. Effects that put the creature in the library or in the graveyard, exile it or instruct you to sacrifice it still apply as usual.
Creatures with Wither and Infect deal damage in the form of -1/-1 counters. If Angelic Overseer gets three or more such counters, it is put in the graveyard when SBA are performed. As this SBA doesn’t have the “destroy” effect, Indestructible won’t help.
Carniflex Demon’s activated ability doesn’t target, so you can put counters on Angelic Overseer with it.
Indestructible isn’t the same as regeneration!
Regeneration is a replacement effect that removes all damage marked on the creature, taps it and removes it from combat (if the creature was in combat) instead of destroying it.
Indestructible is a static ability which effect states that the creature can’t be destroyed. The creature isn’t tapped and stays in combat. All damage marked on this creature stay on it until the cleanup step.
If you cease to control a Human, Angelic Overseer loses Indestructible and is destroyed when SBA are performed if lethal damage is marked on it.
Suppose you control only two creatures: Mirran Crusader and Angelic Overseer. When Magma Phoenix’s triggered ability resolves, every creature is dealt 3 damage. When SBA are performed, Mirran Crusader goes to the graveyard. After that Angelic Overseer is no longer Indestructible and, when SBA are performed for the second time, it goes to the graveyard too. Compare this situation to one in which we cast Day of Judgment.
Final Judgment exiles all creatures. This isn’t a “destroy” effect, and consequently Angelic Overseer is exiled.
*If the effect doesn’t state that the type (or a subtype) is gained in addition to all other types. If so, all types remain.