The Axe is used primarily for defense, but can also be consumed to treat a wound. It is also required for a military event. It is repairable through the Boy Scout Handbook. It weighs 2 slots in scavenging.
Summary: One of the family members that have left the shelter sometime in the past will reveal that they have a wound that has become infected. The player can heat the axe blade to cauterize the wound, but has a very high chance to destroy the axe (needs confirmation, the Axe may always get destroyed) but it can hurt the member. The player can also use a MedKit, but this will immediately consume the MedKit. The member can also leave it untreated, however this has a high chance of getting the character sickened. (exact odds needed, already confirmed that it is possible for them not to get sick). It is recommended not to use anything in this event as there is a chance of the character not to become sick and the player can always use a medkit afterwards.
Summary: Raiders attack and demand the player surrender his/her supplies over to them. If the player uses the poison, there's a high chance of a character getting injured (needs reference). If the player uses the Rifle, there's a very high chance of fending them off without injuries, but it will consume the Rifle's usability. If the player uses the Axe, there's a high chance off fending them off without injuries (Confirmation needed, it may always succeed). If the player doesn't choose anything, the player fights with fists, which gives a low chance of fending the raiders off without injuries, or the family gets beaten up, tied, and the fallout shelter gets plundered.
Summary: If Ted has a full grown beard, there may be a random occurrence of having a choice to shave him with the Axe or not. If shaving Ted succeeds, His appearance will change to the regular stubble he first gets on day 2. If it fails, Ted will get injured(increases Ted's sanity).
Summary: The military will request the player to use his/her axe to chop down some trees to help ease access. Using the axe will have a high chance of consuming its usability.
Summary: The twins will request you to cut down some trees and help build homes. Using the axe will not break. (Needs to be confirmed)