Hi there, you could try this, it has a bunch of suggestions beginning with using a microfiber cloth and vacuuming. Hope it helps! https://homeguides.sfgate.com/clean-wooden-paneling-vinegar-mineral-oil-89999.html
Of course if it's rough hewn raw wood, without a finish, I wouldn't use their suggestion of cleaning with oil. I would vacuum only.
Use Thomasville furniture polish and will give it a nice shine. Walmart carries it
I would use a flat mop with a microfiber cover that is slightly damp and run it across the walls just like you would the floor
I vacuum ours with the dusting brush attached. It does work, but it takes awhile to get it done
best dusting/cleaning kit you can buy I use this on my wood paneling, no chemicals, dust sticks on these just shake them out to remove(outside) dust and wash the cloths reg. wash (no fabric softener) they'll last forever https://www.qvc.com/qvc.product.V36109.html?colorId=HB8&sizeId=000&ref=GBA&cm_mmc=GOOGLESHOPPINGFEED-_-GShopping|M|Generic|home+improvement|vacuums+cleaning-_-pla-_-sroGtw3rp|dc_44906292707_pla-646343420345__V36109-HB8-000_&mkwid=sroGtw3rp|dc_pcrid_44906292707_646343420345_pkw__pmt__productid_V36109-HB8-000&gclid=EAIaIQobChMI1vnjuuyM4wIVGh6tBh2A4weaEAYYASABEgIwsfD_BwE more https://www.amazon.com/Microfiber-Dusters-CAMPANELLI-Extension-PuppyFur/dp/B07JN6TC7T one more https://www.amazon.com/Extendable-Cleaning-Microfiber-telescopic-including/dp/B078GWH7C6/ref=pd_lpo_sbs_121_t_1?_encoding=UTF8&psc=1&refRID=5YTYK764G59WG8EDQE08