Check your src/package.xml file, and make sure your standard objects and custom objects are actually listed in the file:
IF not, you can manually edit this file, or go in to Project Properties > Force.com > Metadata, then "Change" it, click the refresh button (two arrows pointing in a circle), then select the objects you want.
Custom fields appear as part of the CustomObject file, but if your schema is not in sync, you'll often get an empty CustomObject file that looks like this:
<?xml version="1.0" encoding="utf-8"?>
<CustomObject xmlns="http://soap.sforce.com/2006/04/metadata" />
If it looks like this, then your schema is out of date, and you need to do the refresh again.