This is theme dependant. If your theme is setting new or sale products with a specific CSS class then you can search your template files for this class or any other text with a grep command i.e. if you can see that your new products have a class of newproduct then goto the command line, change into the template folder of your frontend theme and then use
grep -irl newproduct *
to find all instances of this text in your themes template files. This will help you locate where your theme is rendering this data.
It is however more likely that your theme references another module method that performs the logic to decide if a product is new, or on sale. Then you will also need to look in your app/local or app/community folders for the module that is performing the logic to find where the html is being created.
Hope this helps.