Can an oracle take Arcane Strike? Different revelations and mysteries allow an oracle to cast many arcane spells. I do not see how the feat language disqualifies an oracle.
If an oracle can take arcane strike, how would one determine caster level (oracle's level? highest arcane spell level?)
The fact that spell x appears on spell list of arcane caster does not make divine caster with access to the same spell arcane caster or vice versa - all spells cast by Oracle are by definition divine so no, Oracle cannot take Arcane Strike feat.
Right. As an example in the other direction, until the APG, the only class that was not divine that got Cure Light Wounds was the bard. Bards did not have access to a divine spell, they had an arcane version of CLW.
Similarly, a cleric with the fire domain gets fireball. They aren't casting an arcane spell, they get a divine version of fireball.
This all said, DM might decide to change Arcane Strike into Magic Strike and let it work with divine spells if he wished so. This could be a little bit unbalanced with Paladin or Ranger, however, can't really say without some tests.
If wanted to make it work it would be fine. And It would not be unbalanced cause the earlest that you could get it would be 5th level
and if you do not have magic weapon by then that in it self is wrong.
Cause this is realy week feat. Caue it will not stake with magic item, so big deal.
The only way I think could be broke is that you could take +1 weapon and +9 worth of other enchancements that do not count as pluss to hit. Like Fire, Holy, Cold, ect. And still have + 5 to hit.
It does stack with magic weapon - it is untyped bonus to weapon damage, not enhancement so at 18th level Paladin/Ranger allowed to use it gains +4 damage on every attack made for 1 round (so it includes opportunity attacks) at the expense of swift action and one feat.
No.
Oracles do not cast arcane spells. They cast divine spells from the spell lists of arcane casters.
Is this also true for the Ancient Lorekeeper archetype bonus spells that are drawn from the wizard/sorcerer spell lists?
In other words, are these bonus spells divine or arcane?
Anything an Oracle gets through the Oracle class is divine.
The only way to get Arcane Strike as a divine caster is to have an 'arcane' spell-like ability. If you do, and you use it to take Arcane Strike, then by the rules any caster levels you possess in any way will improve Arcane Strike.
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Spell-Like Abilities: How do I know whether a spell-like ability is arcane or divine?
The universal monster rules for spell-like abilities states: "Some spell-like abilities duplicate spells that work differently when cast by characters of different classes. A monster's spell-like abilities are presumed to be the sorcerer/wizard versions. If the spell in question is not a sorcerer/wizard spell, then default to cleric, druid, bard, paladin, and ranger, in that order."
For spell-like abilities gained from a creature's race or type (including PC races), the same rule should apply: the creature's spell-like abilities are presumed to be the sorcerer/wizard versions. If the spell in question is not a sorcerer/wizard spell, then default to cleric, druid, bard, paladin, and ranger, in that order.
For spell-like abiities gained from a class, use the spell type (arcane or divine) of that class to determine whether the spell-like ability is arcane or divine. If the class doesn't cast spells, use the above rule for spell-like abilities from race or type.
Edit 7/15/13: Wording changed match the precedent in the universal monster rules for spell-like abilities.
Edit 9/23/13: Wording updated to clarify racial/type SLAs vs. class SLAs.
If instead you get a spell, from what spell list you get the spell slots to cat it?
If you use oracle spell slots it is an oracle, and so divine, spell.
The only way to get Arcane Strike as a divine caster is to have an 'arcane' spell-like ability.
To expand on that in line with my previous statement that it can't come from a divine class, the spell-like ability can't come from a divine class. If you have something like an Aasimar Oracle with the Alter Self spell-like ability from race, then it's arcane and you can qualify.