Linking your website to some pages that located in the specific countries you need , would help you a lot.
many countries = different languages, right? translate your content and have a multilingual website. how to place keywords in your articles I decribed here: https://forums.digitalpoint.com/threads/where-and-how-to-place-keyword-in-article.2666261/#post-18650133 with this strategy I'm getting expected results... for my sites at least...
just go to alexa website check country wise top 500 website and be concentrating on them , you can find best results .
As you are targeting many countries so you have to build country specific links, your site quality should be good, you should mention country name on your web page, title, heading etc. It works.
I presume you own a Top level domain and this wont work with country level domain. domain[dot]com (Your main site with USA & International Rankings) domain[dot]com/Uk (United Kingdom) domain[dot]com/de (Germany) domain[dot]com/in (India) domain[dot]com/au (Australia) domain[dot]com/Sa (South Africa) domain[dot]/fr (french) domain[dot]/etc (country) Each sub directory consists of its own Sitemap and related content. After doing the above add each subdirectory into Webmasters tools, verify it and target them accordingly. By doing this you're telling Google to identify each Sub directory to target particular country. Other way around to target different countries is by using Sub-domains. (I don't recommend it.) When you choose sub-domain Google count's it as a different site and won't show all pages index of the domain (only sub-domain pages will be shown). On the other hand while using sub directory, each sub directory will be considered as a part of the site itself. The more quality pages indexed the more authority of The DOMAIN and Trust factor. Hope this helps. BigSEOpro
Create multiple versions of your content, one in each language(don't use Google translate). Hire some translators, get backlinks to your content(in *language*) from sites in (country for *language*). You can use RankTracker from Link-Assist.com to check your rank in each country specific search engine(google norway, uk, us , china etc)