Today, discourse on climate change seemingly tends to focus on earthly elements such as pollution and human activity. While I am certainly not well-read on climate change research, after inspiration from a physics teacher's example of a baseball bat's center of gravity, and from reading this Stack Exchange post, I was curious about how the Sun's oscillation might play into our planet's entire climate activity. Have scientists even considered this information in determining the cause of climate change? Due to its elliptical orbit, Earth's distance from the sun changes, but wouldn't the Sun's oscillation affect what parameters this distance shall be over time?
I'll get you started at least, this is a bit too broad otherwise; I guess what you're describing are called Milanković (Milankovitch) cycles. Are climatologists aware of these? Yes, for a long time. Milanković published his first paper on the subject, Theorie Mathematique des Phenomenes Thermiques produits par la Radiation Solaire, in 1920. As for Solar oscillations in general, even much longer periodicity of ~ 26 million years of the Sun's oscillation about the galactic plane has been considered before (in 1984). As we're aware of the 11 year solar cycles, and have been integrated into climate models that climatologists work with, including collective effects of all of these manifesting in grand minima and maxima of solar activity (PDF).