Magic Items

Wondrous item, uncommon

This small sphere of thick glass weighs 1 pound. If you are within 60 feet of it, you can speak its command word and cause it to emanate the light or daylight spell. Once used, the daylight effect can't be used again until the next dawn.

You can speak another command word as an action to make the illuminated globe rise into the air and float no more than 5 feet off the ground. The globe hovers in this way until you or another creature grasps it. If you move more than 60 feet from the hovering globe, it follows you until it is within 60 feet of you. It takes the shortest route to do so. If prevented from moving, the globe sinks gently to the ground and becomes inactive, and its light winks out.

Wondrous item, uncommon

This gem contains a mote of elemental energy. When you use an action to break the gem, an elemental is summoned as if you had cast the conjure elemental spell, and the gem's magic is lost. The type of gem determines the elemental summoned by the spell.

Blue Sapphire Air elemental

Wondrous item, very rare (requires attunement)

This belt is made from plates of steel embossed with golden filigree connected by metal pins. A fire giants face adorns the buckle. The giant appears to be having a hearty laugh as she wears an enormous smile on her face.

While wearing this belt, your Strength score changes to 25. The item has no effect on you if your Strength without the belt is equal to or greater than 25.

Cape of Enlargement

Wondrous item, very rare (requires attunement)
Ancient runes are stitched in silver thread along the hem of this grayish-purple cape.

The cape has 3 charges. As a bonus action while wearing the cape, you can expend 1 of its charges to enlarge yourself, granting yourself the following benefits:

Your size increases by one category—from Medium to Large, for example. If there isn't enough room for your size to increase by one category, you instead become the maximum possible size in the space available.
You have advantage on Strength checks and Strength saving throws.
When you hit with an attack roll using a weapon or an unarmed strike, you can add your proficiency bonus to the attack's damage.
These benefits last for 10 minutes or until you use another bonus action to dismiss them. The cape regains 1d3 expended charges daily at dawn.

Weapon, very rare

You have a +2 bonus to attack and damage rolls made with this magic weapon.

From the Adventure:

The headsman has his gigantic +2 greataxe at hand—a weapon that can be employed only by a creature at least as strong and massive as he is. (25 strength, Huge) He has a +13 bonus to hit with the weapon, and it deals 28 (3d12 + 9) slashing damage on a hit.

From Adaption Guide

SPECIAL MAGIC ITEMS
Several examples exist inside the pages of Against the Giants that have abilities above and beyond those abilities normally located in the Player’s Handbook and Dungeon Master’s Guide. (...)
Headsman’s axe. This is a Very Rare magic.