Certain practices can help discourage deposits of dirt and grease from forming in the first place. One method is to grease the grates of your hot grill with a little cooking oil right before your start cooking. In the same vein, scrubbing your grill grates with a raw onion is another tactic you can try. If you do have a grill brush without bristles, it's a good idea to scrape your hot grates both before and after grilling.
While the grill grates and flavorizer bars are removed and soaking, tackle the caked-on gunk in the firebox. Put another bucket underneath the firebox where the grease tray sits to collect debris. The easiest way to start is with a wet/dry shop vacuum, whether full-size or a portable, like Milwaukee’s M18 hand vacuum. Since wet/dry vacs are mostly workshop items, you won’t feel bad about using one to suck up the gunk that’s collected in your grill. You can use the grill brush to help loosen stubborn stuck-on grit. If the deposits are really caked on, dip the wire brush in the bucket of soapy water and get to work. Use a hose to rinse it out when it’s clean.
Seasoning a grill has no relationship to seasoning the steak or eggplant you're grilling. In the latter case, you season to add flavor to the raw food item. But when you season a cast iron grill, you're not adding flavor. It actually refers to the process of coating the grill grate with oil, then heating it, to render it rustproof and create a virtually nonstick surface. Depending on the type of grill you own, you may only need to season the grill the first time you use it and occasionally after that. And with a Weber brand grill, you may not need to season it at all.
Clean the bottom of the grill with a soapy sponge. Once all the chunks are gone, scrub the bottom with a sponge or scouring pad and soapy water to remove any built up grease or grime. Lots of drippings and food scraps tend to build up under the burners of the grill. Pay close attention to this area and clean it as much as possible to avoid corrosion.