These are the laws that even Gods must follow otherwise the fates will punish you accordingly. It may be making you powerless for a fixed time, taking away your powers when you really need them, anything. These are not oaths on Styx that can be easily broken but laws for divine.
Some of these laws are-
A god cannot enter another god's domain-
This has a condition, if you share the domain then you can enter. Like Poseidon can enter a river god's domain but Zeus cannot because as all big bodies of water are Poseidon's domain.
A god cannot sit on another god's Throne or touch his Symbol of Power-
There throne is like a bank where their godly energy is stored, if they are damaged too much, then gods start losing their energy. Effective for both god's and titans. Almost every divine being follow this as they cannot store so much energy in their body, only beings on Primordial level can, and their power far surpasses normal god's.
A Symbol of Power is the weapon by which the god's impose their will on the mortal world. A god cannot directly touch other gods Symbol of Power but it does not mean they cannot be replicated and then used, which is what Zeus feared the most in Lightning Thief.
God's cannot interfere in their demigod children's life-
They cannot raise them and all that but they can meet them time to time. For example, Nico can live in Underworld but have minimum interaction with Hades as he cannot raise him.
No interference in quest-
God's cannot do anything to help or interrupt a demigod's quest directly. Indirectly if the demigod sacrifices something valuable, like Nemean lion pelt, hydra pelt or something then they could help but only in limited way. For interrupting, gods generally send a monster.
A quest is never free-
If a god issue a quest personally, like Ares asking for the shield in books, then they must reward them somehow, like Ares did with ride and rations. And if a quest has a prophecy behind it, like all the canon quests, then the Olympian council or their godly parent will reward them. So, no you cannot just have a quest and say your reward is me letting you live.
A god cannot fight a mortal in their true form-
A god in his true form are too strong and fast for it to be a fair fight. So, if a mortal challenges a god, then he will fight in a restrained form that is generally a humanoid form and is very limited.
In this form they are greatly restricted in speed, reflexes, strength, and godly powers. They are still far superior to mortals, like Hermes can defeat Ussain Bolt or fastest marathon runner without breaking a sweat.
This is only good for children of big 3 against a god with no elemental or magical domain they can use, like Ares. And even then, they may have to use tricks.