The legal relationship with your sister-in-law is that she is the wife of your brother or the sister of your spouse. That does not give you any legal rights in her life or her any legal rights in your life. It does mean that you are both part of an extended family, but that is more cultural than legal.
No, there is no relationship between the two of you other than what you stated in the question. The introduction would be, "This is Tom Jones, the brother of my sister's husband."
Your Wife or Husband's Sister
They are sisters in law.
There is no relationship. You do not share a common ancestor. The connection is simply through marriage.
Brother-in-law
Your wife's brother is your brother-in-law.
Sister in law
They were brother and sisters.=Mary was born first. Then Elizabeth and Edward last.=
The brothers of your spouse are your brothers-in-law. Also, the husbands of your sisters are your brothers-in-law.
Let's see if we can unravel this. Your sister's husband's father's brother is your sister's husband's uncle. The uncle's daughter is your sister's husband's cousin. There is no relationship to your sister, unless your sister wants to call her a cousin-in-law. To break it down to its simplest terms: She is your brother-in-law's cousin and no relationship to you.
Of course you could. But you're implying to incest and this is definitely not incest.
Your sisters grandson would be your grandnephew.
Sisters
Sisters.