I have a ton of furniture and possessions and I'm quite dismayed about what to do. 

We glue down vinyl and find that tenants can mop it, spill on it, drag furniture on it and it holds up pretty well

Nothing to worry about yet.Your property has an additional bedroom that will appeal to larger families with 4 or more children or live in grand parents while your neighbors are only 4 bedrooms.It actually makes a huge difference because your property will have a different customer base for the most part.Stage your property properly with the right furniture and decorative items and really get it looking far superior than the neighbors home.

My home is currently a literal construction site and my fenced in back yard is full of debris, rusty nails, ladders left propped up against the walls and my patio furniture and BBQ grill thrown about as if they were trash.

Writing offers is a serious business - you need to know and understand every word in that offer and most importantly -- you need to understand disclosures and have a sense of fairness.Also understand that agents DO NOT write contracts (unless they are lawyers) they can ONLY fill in the blanks on a standard approved contract of sale (usually 20-35 pages).You can design your own contract if you are presenting yourself.When making offers nationwide -I always have "Hybrid" clause (sellers love this)Use banking days (nothing goes as expected in real estate deals - you need time to get to the profit)A built-In extension (you need time and don't want to beg for an extension.)Financing clauses - (the sweeter you can make the deal - the easier it will be to assign your contract - we call it CONTRACT CANDY - ask for everything - the furniture - car in the garage - lawn equipment - money back at settlement - paint the house - delayed settlement etc.)A memorandum of understanding - sellers need to understand your motivation and what you are trying to accomplish and who you are - do you have a license, bonded, insured - references - testimonials - etc. remember you are a buyer - sellers look to you to satisfy their financial needs or real estate problems - don't be cavalier about your actions - leave ego at home.  

Other kinds of storage are much easier to add via drawers on the floor of the closet or furniture.

Regardless of affiliation to Tenant any guest which: (a) stays on the property or in the Premises more than Fourteen (14) days or nights in any 6 month period; or (b) receives mail at the Premises; or (c) moves in their own furniture; or (d) pays Tenant’s rent; or (e) claims Premises as their residence, will be considered a tenant, rather than a guest, and must be added to the lease agreement; otherwise it is considered a lease violation and Landlord has the right to terminate this lease.

Unless its in florida law or your lease a wire rack in the closet is the same as furniture.

They have moved out the furniture but are unable to move out remaining personal items (kitchen, bathroom, random small pieces).

You don't want to spend a bunch of money buying furnitures, only to be shutdown later.