Debt paydown is the fastest way to improve your credit. The impact will vary. It depends on your utilization change. For example, if you were maxed out at $15k, then paying it to $5k will have a moderate impact on your FICO, certainly double-digit potential (YMMV on your credit, how they reported, and whether or not util was a negative scoring factor). Conversely if you had $150k in revolving credit and you went down from 10% to 3%, then you'd see smaller gains.
Close? It's up to you. Ideally you'd want to leave them open and not use them until you can get your debt down further. Maybe put a small utility on each or just sock-drawer them for a while. IMO, the only time you want to consider closing them is due to fees.