(やくそく) To make a promise.   $$$
(ちかう) A vow. Like at a swearing-in ceremony or when you visit a temple to promise / ask God for something. Stronger than 約束. The first time you got caught cheating, you’d make a 約束 to not cheat, But the second time you get caught, you have to 誓う!!! Has a feeling of trying to salvage what’s left of your credibility.
(ちぎり) A noun, never used in verb form (契る). It has the same kanji as contract- a 契り requires two people to pledge something to each other. An engagement.
(せいやくしょ) An oath which is recited from a script, and  made at a specific ceremony:, swearing-ins, initiations, etc. Compare this to 誓う, which can be different according to the situation:“I swear I’m not lying!” “It wasn’t me, I swear!”