My experience with situations like this are that they are usually electrical in nature. Check ALL your major grounding points, especially the ground for any engine sensors and the ECM/ECU. This is a simple issue but can make your life difficult. This is s simple job and costs almost nothing to do so do it first. Remove and clean all connectors with fine sandpaper. Clean with a paper towel and carb cleaner. Let dry. Coat with silicone grease and re-assemble. This may work wonders on your car.
Then there is the possibility of the fuel pump. Sometimes they will cause poor performance without a check engine light. Then there are the O2 sensors. I have had them just about gone but no code was being thrown. The only time I have seen an O2 sensor code is when the sensor wiring was severed. When where the sensors last changed? Are they far overdue?
Have the car scanned for any PENDING codes. You won't have a check engine light.... YET with pending codes.
Checking the valve lash is a good idea as well. Honda lifters need adjustment from time to time. Look in your manual. Are you overdue? This can cause burned valves as well so do not neglect this.