To start off with: Your space just isn't very good for the task you're using it for (RPGs). There are some things you can do to help out, but ultimately change is something you'll want to strongly consider.
You're going to want to specialize your table for what it's good at. Which is providing a stable space which most players can see.
This means that your maps go on the table (at least the ones currently in use), and food rests on the table while it's not in use.
People should plan on actually eating with their food on their laps. The bowls / glasses / etc. just rest on the table when hands are needed for other things.
Empty plates/glasses/etc. should move to the floor, and/or be disposed of.
Food "reservoirs" (drink pitchers, casserole dishes, pizza boxes, etc.) go in the kitchen. If you want more food/drink, you walk out and get it.
Books should be stored on the floor, or in backpacks when not in use. An exception can be made for very frequently referenced books (back in my small table days the core book for Star Wars D6 lived on the table, because it was referenced whenever someone took damage).
Character sheets should generally be kept with the player on the player's lap or the floor near them. Use clip boards or hard cover books for support while writing.
For die rolls, make sure everyone has a box top to roll dice into within arm's reach. This way they can roll without chasing dice across the (crowded) table.
You will still tend to have a certain amount of cross-talk with this setup. Cross-talk is always something that the group itself controls, but having people at different levels and different planes within the room does encourage it.
I'm also not really sure how to herd a group into doing any of this. Back in my days of playing on small tables, the group tended to gravitate to doing this sort of thing pretty naturally.
Buy yourself a folding table. It's cheap, and it uses very little storage space. Pull it out when you game.
Hopefully you have chairs around the house that can be moved to the table for game night. If not, folding chairs are an option... Although they use an awkward amount of storage space.
This will give you a bit more space, and make that space easier to use. It's also much easier to supplement this space with end tables and TV trays (which are often a bit high for use with a coffee table).
You'll still want to keep things like pitchers, pizza boxes, and other food reserves in the kitchen. And books should probably still live off the table when not actively being used.
Finally, sitting everyone down at a single table helps discourage cross-talk. It doesn't eliminate it... It's not magic. But having everyone at a single table, focused on the game, and sitting forward in their chairs does help quite a lot.
Ideally, you would want to have an actual table and chairs for play. Either as part of a dining room, or a dedicated gaming space. It's more stable, you can make sure the lighting is better, permanent tables tend to be larger than folding ones, and it's just nicer to have tools built for the job at hand.
The big downside here is that furniture is expensive, and eats a lot of space. Depending on your living conditions, this may simply not be practical for you.
No matter what you do, keep a roll of paper towels handy. Spills happen, regardless of what precautions you take.
Designated food breaks can work for some groups, but I find they often don't. It isn't unusual for there to be one or two people who arrive at the game directly from something else, and need to either delay the game or eat at the table.
NO FOOD AT THE TABLE rules tend to break down for the above reason. Also, sometimes there are cookies.