Runic Axe is a really weird card. The first thing you have to figure out is who it's intended for. At level 0, that's just anyone who needs to kill things. It's a +1/+1 weapon that has limited but regenerating charges, and which lets you spend them optionally, so you don't need to overkill odd health enemies. That's a machete but with charges, or a .45 that regenerates bullets. The other drawback is it takes a second hand slot, so that's not ideal. But hey, it's competitive with the best level 0 weapons, so yay. Totally normal, reasonable weapon for fighter types, or flexes who don't need their hands.
When you level it up, it gets weirder. Either you leave it as a 2 damage weapon and you never get combat upgrades, or you want to do 3+ damage and take Ancient Power. Ancient Power, however, just pushes the limitation slightly upstream. Now you can do 4 damage attack with it, but only once, and then again once next turn (assuming you take Saga), and then you have a dead round before you can do it again. Meanwhile, no other swing you take can spend any charges. The practical implication of this is that your 10 xp pair of weapons only give you 2 bonus damage every round, and you paid 3 xp to compress that damage into a single action (and having the option to frontload 4 damage in one action, if you're full of charges) instead of two actions. If you take Scriptweaver, you get crazy accuracy in addition to your damage, but that's it. If you don't, you'll find yourself never having the charges to do anything but +damage.
If you're interesting in frontloading damage, or in getting a lot of bonus damage on one card you'd be better off with a Flamethrower. That grants 3 bonus damage per attack for 4 attacks, and the Axe won't catch up in total damage for 4 rounds. If you just want sustainable damage, Cyclopean Hammer offers a moderate hit bonus and a change of 3 damage (1/round) as well as the chance to "solve" an enemy by just bonking it to a location you don't care about. So the fully upgraded combat Axe is for someone who wants to be really good at combat like one swing every other round, will spend 10 xp for it, and doesn't need their hands. I don't know who that is. Crazy accuracy and 4 damage is equivalent to like 2 swings from a decent level 0 weapon with some discards to make sure you hit. That's not a lot of bang for your 10 xp.
So let's not build the Axe as a pure combat tool. Let's see what else we can do with it. Fury is a really neat, repeatable AOE damage effect apparently designed to counter swarms in Dream Eaters, so that's one thing we could do. Glory is a way to make yourself more sustainable. If you're Mark Harrigan, you can even take the heal, use Sophie on something, and get both the +2 to a test and the extra card. Carolyn Fern could use the horror option, but she's not allowed to use xp weapons so forget that. Glory is probably a situational, niche imbue. Elders lets you get a clue if you beat an enemy by the shroud, so you could be like Roland-lite. The issue you then run into is that even with Scriptweaver, you can only pick 2 of: try to get clues, do 2 damage to efficiently eliminate the enemy, get a bonus to have a reasonable chance at succeeding by shroud. If the only enemy you need to deal with is Swarm of Rats, you could just go Elders/Accuracy a couple of times and beat multiple clues out of them, but that's another niche use, not your Plan A.
So where does that leave us? Hunt. Hunt is really good. Fighters' typical gameplan is do incredible amounts of damage in order to defeat monsters before they inflict damage to the investigators, and they typically pay through the nose for it, in terms of xp, resources, support cards, and often ammo. Atomizing monsters is often the sole thing they're good at. As such, any action spent NOT atomizing monsters is the worst feeling in the game for them, especially moving to the next monster, or engaging that aloof enemy, or the one eating the Seeker who will otherwise die if you draw the auto-fail. Axe users with Hunt don't care about that. They can pull enemies to a connecting location, or move to an enemy at a connecting location, or engage an aloof enemy, and then do their murdering. It solves a couple different problems that otherwise would require a combination of things like Fang of Tyr'thrha, Telescopic Sight, Safeguard, and for some fighters, Shortcut. Free movement, free engages come at hefty premiums. The Runic Axe solves that for you. It also solves the problem of concealed enemies fairly handily, since they all spawn in a tight radius, would be impractical to expose with ammo, and you can spend your second imbue on Accuracy for those high shroud locations.
I dunno, there might be a better use for the Axe, but it seems fairly narrowly tailored for Scarlet Keys, and for fighters who want to be equally good at movement instead of just outrageously good at fighting, so also campaigns that incentivize movement pretty hard (but still fighting, because the axe is no faster than walking yourself, it just lets you combine the move and attack actions).