I hold an Indian passport and have an F-1 Visa (multiple entry) for USA. I applied for a Schengen visa and it got approved but the Italian consulate has affixed the schengen visa sticker in a page which comes before my US Visa. For example, my US Visa sticker is in page 20 while my Schengen Visa is now in page 15. Does this mean that now I can only receive entry stamps for entering US from pages 16 to 19 only? Or can I get stamps anywhere in the Passport as long as there is an empty page.
The immigration officers can stamp anywhere there's space. Generally they'll prefer to stamp somewhere near the visa that's being used. But if your passport is full enough that they have to flip a few pages to find space, they can do so. Whether the pages they have to flip past are filled with visa stickers or with stamps doesn't make a difference.
If there really is no space at all, all pages are full, you need to apply for a new passport. In some countries (maybe most) you can apply for a passport with an extra large number of pages. Also in some countries you may qualify for a second passport (perhaps called a "business passport"), which is a secondary passport that you keep next to your current passport but use for business travel; this is particularly useful because you can still travel with passport A when passport B is being processed at the embassy of Turkmenistan. There are also countries that deny entry (or worse) if the passport shows evidence of having visited another country (or region of country), which can be avoided with two passports.