“To cook up” can mean just to cook some food, especially for others.

“Sarah cooked up a feast for us.”

It can also mean to plan or invent something, usually something a little dishonest.

“Jerry cooked up an excuse for being late.”

“Mary cooked up a scheme to cheat her employer.”

 

To be “at odds” means to be in conflict or disagreement.

Two people are “at odds”

“Joan and Anna are at odds.”

One person is “at odds” with another.

“Joan is at odds with Anna.”

Two people are “at odds” over an issue.

“Joan and Anna are at odds over the way to organize the project.”

” Joan is at odds with Anna over the way to organize the project”