The first level ability of a Paladin is Divine Sense.
The presence of strong evil registers on your senses like a noxious odor, and powerful good rings like heavenly music in your ears. As an action, you can open your awareness to detect such forces. Until the end of your next turn, you know the location of any celestial, fiend, or undead within 60 feet of you that is not behind total cover. You know the type (celestial, fiend, or undead) of any being whose presence you sense, but not its identity...
So by Divine Sense undead are either strong evil or powerful good. To narrow it down more we can look at the Oath of Devotion’s Turn Unholy
Turn the Unholy. As an action, you present your holy symbol and speak a prayer censuring fiends and undead, using your Channel Divinity. Each fiend or undead that can see or hear you within 30 feet of you must make a Wisdom saving throw. If the creature fails its saving throw, it is turned for 1 minute or until it takes damage.
Turn Unholy doesn’t allow the Paladin to differentiate or choose which undead or fiends are effected. So Turn Unholy states all fiends and undead are unholy.
From those two abilities of the Paladin it appears that at least an Oath of Devotion Paladin would see all undead as Unholy and Strong Evil.
But it is up to your DM, as he will be the god judging your actions.