It's a neat idea... but it probably wouldn't, and shouldn't, work, for a couple of reasons:

1. That's just not how magic item creation works in D&D.

As the rules quoted by Red Wullf say, you have to be a spellcaster to create a magic item in D&D. So unless your group is willing to introduce their own custom house rules for magic item creation, it just won't work. Your fighter can scribble anything they want on their sword, but at the end, without a spellcaster to help them, they won't have a magic sword, but just an ordinary sword with scribbles on it.

2. If it was that easy, everybody would do it.

Even if I were to introduce a house rule to allow enchanting items like this, I wouldn't let simply copying the runes on another item accomplish anything but the most minor enchantments.

Why not? Well, if you could enchant items like this, so could anyone else with a reasonably steady hand. If a fighter can carve runes on their weapon to enchant it, so could the blacksmith that forged it in the first place. So if enchanting items was this simple, everybody should be walking around with runes on their weapons (and probably everything else they own).

Conversely, if you want powerful enchantments to remain rare (and I presume you do; it would just be silly to have every random NPC walking around with a Flaming Ethereal Armor-Piercing Impervious Returning Holy Stunning Keen Extensible Soul-Sucking +11 sword of Triple Damage vs. Everything), there has to be some reason why not just anybody can create them by copying another enchantment. The two obvious explanations are that either:

• it's difficult to copy advanced enchantments — so difficult that only people with extensive practice (i.e. high level in a suitable class) can hope to accomplish it reliably, or

• it takes something more than just the right runes to enchant an item — perhaps the runes only serve to bind whatever being or force is powering the enchantment to the item, but do nothing else on their own.

Thus, sure, I'd be happy to house-rule that something like, say, a minor enchantment against rust could be applied to a weapon just by copying the runes off another weapon; this would then be a standard feature of any weapons of decent quality. Or I could easily see anyone with a bit of skill being able to inscribe the correct runes on a clay amulet to protect its wearer from evil spirits — you know, those ubiquitous evil spirits that will surely get you if you go out without a protective charm, which is why everybody has at least half a dozen such trinkets on them at all times. In short, the kinds of things that make for neat setting detail, but which don't really have a massive effect on game balance.

But if you just tried to copy the runes on a powerful magic sword onto a lesser blade, without any special understanding of what you were doing, then the only reasonable outcomes I can see would be either that they just wouldn't work (because you did them wrong, or because some other essential component is missing), or possibly that they would work, but not quite the way you intended... probably leaving you with a cursed weapon, and an object lesson in why mere laypeople should not dabble in magic. ;-)

There are several options you may pursue as a DM to achieve this goal but keep in mind that homebrewing a mechanic for this might bog down, unbalance or leave wide plot/lore implications in your game that might be exploited.

Magical Effects

• Modified Reincarnate

  You may use a modified version of the reincarnate spell as a way of explaining how 3 owls turned into an elf. Perhaps an archfey had 3 favoured owls as pets. When tragedy struck one day (maybe when a powerful ogre-magi and its army invaded), the archfey's last act was to reincarnate the owls as a vengeful elf.

• Wish

  Perhaps a wish spell was the cause of that character's origin. An adventurer might have come across a genie and wished for a companion with the wisdom of 3 owls.

• Wild Magic

  The effects of wild magic was responsible for bringing back Minsc and Boo about a century after his death in the D&D Comics. It wouldn't be too much of a stretch to believe that wild magic could transform 3 owls into an elf. A wild magic sorcerer might have been responsible as he or she was practicing casting polymorph.

Will of the gods?

Perhaps the gods needed an agent to carry out their will. Just as Zeus in ancient mythology was said to have changed ants into men. Maybe a god in D&D whose high priest had recently become corrupted might have chosen 3 watchful owls to turn into a single elf with qualities that the god cherishes.

Madness

Maybe that character is just mad - full on nuts! In the DMG on pg 258 guidelines for dealing with madness in characters can be found. She could roleplay her madness as a character flaw; as someone who sincerely believes she's 3 owls when really she's just a crazy elf.

As a plot hook, you might decide that her madness comes from a curse, perhaps cast upon her by a shadow-druid when she accidentally started a forest fire as a child.

Have Fun

This has potential to be quite a memorable character. I recommend you do not add in mechanical changes such as giving the character special owl powers, because it might unbalance the game. Focus on the narrative, background and role-play aspects to bring this character to life.