The likelihood of your code being incompatible with Java 8 is slim, since Java has taken great strides to ensure backwards compatibility with all previous versions.
The issues that you'll likely run into lie much deeper, likely in implementations of collections or methods who have changed over the years.
If you don't have a test suite that covers the critical paths of your code, start there. You'll need that test suite to ensure that the migration hasn't horribly broken anything.
Next, peruse the compatibility guides for Java 1.7 and Java 1.8 and be sure that nothing that you're using in particular is impacted by those changes.
Lastly, the code cleanup piece can be tackled, but it shouldn't be addressed right now. The only thing you need to concern yourself with is to get the platform running on the new version of Java. As you work in the code base, discipline yourself and the team to use the newer Java idioms, such as the diamond notation, and try-with-resources where applicable.