Orbital parameters, such as precession of the equinoxes and orbital obliquity affect climate but on time scales of 10s of 1000s of years. They have negligible effect on present climate, where decades are the important time unit.
If you interested in the orbital parameters and Greenhouse Gas concentrations for various time slices and periods of the past, you may search for "PMIP4" (Paleoclimate Modelling Intercomparison Project #4). In the framework of this project, all these parameters from various studies have been put together. For example, you may go https://www.geosci-model-dev.net/special_issue12_888.html to see the publicly available studies regarding the design of studies for various past time periods. Please note, there are many more publications, special issues, and reports available.
How do these values influence the climate? To answer these questions you may turn to the former PMIP studies or check the IPCC reports, which offer a comprehensive view of our knowledge; here you may go to https://www.ipcc.ch/report/ar5/wg1/information-from-paleoclimate-archives .