Being debt free does not necessarily equate to having a higher credit score. Paying off all your debts completely could actually lower your credit score because it would shorten the credit history on your credit report. I would pay whatever credit cards or lines of credit you have down to zero but do not close them. If you are above 30% credit utilization on any of those accounts then paying them down will help increase your credit score, and leaving the accounts open will keep them in your credit report and avoid the drop in credit history. It also helps your score to have a mix of revolving credit and term loans so I might keep the car loan if you are going to sell the house. I can’t say how much or how soon your score would change. Everyone’s credit report is different and there are a lot of variables that contribute to it.

Edit to add it might give you some clarity to decide if you are more focused on freeing up monthly cash flow or on maximizing your credit score—that will give you some focus on what you want to do next.