What organizations have some oversight on euthanasia?

Question

organizations that have control or power over controlling euthanasia choices and the laws that govern this ethical issue

Answer 1

Only legislatures and the courts have control over what laws exist.

As far as euthanasia, no US states and very few countries allow it. Remember that euthanasia is different than assisted suicide. For euthanasia, the doctor (or whoever) takes the physical action that terminates the life. In assisted suicide, the doctor only provides the means, and the person ends their own life.

In the US, only Oregon currently has assisted suicide laws. The federal FDA tried to overrule the Oregon legislature, but the courts ruled that it was a matter for the Oregon voters, not the Attorney General, to decide.

So, as far as organizations that have control over whether one person is allowed to actively kill another, for whatever reason -- the hospital (if any), the state medical licensing board, the appropriate state legislature, and the federal government, in roughly that order. As far as assisted suicide, only the appropriate state legislature.