It seems that the term "strong balance sheet" is somewhat subjective in nature and requires the inter-relationship of all the financial statements and a better than average knowledge the company and its sector.

This is true, but don't let it stop you. I recommend choosing a company you like, or are familiar with, even just a place you like to shop.

Read their 10-Ks and 10-Qs:

http://www.sec.gov/edgar/searchedgar/companysearch.html

Start with the most recent 10-K (there's a lot more detail and background in those, than in the quarterlies). Eventually some things will become clear, and other questions will arise. Re-reading with these questions in mind (and using full-text search) helps a lot.

The other thing I'd recommend is to think of your own personal balance sheet. Without getting into accounting arcana, you have a common sense, gut feel for what comprises a "good" b/s. Businesses are more complex, but the same fundamentals apply. Take in more cash than you spend, don't run out of liquidity.

Hope this helps.
-joe