Are there any territories of EU member states that are located inside or outside of Europe, but are not part of the Schengen Area?
There are territories of the EU member states that are excluded from the Schengen Area. There are two types of such territories: territories, which are outside of Europe and remote islands in Europe.
Most of the territories that are outside Europe (for example, French Guiana) are part of the EU, but they are not part of the Schengen Area, meaning that each of them conducts border controls and requires a visa, if applicable.
Also, you should keep in mind that the Norwegian island of Svalbard is not a part of the Schengen Area and it does not have any visa regime. In order to enter or leave Svalbard, personal checks are performed individually.
With respect to Denmark you should be aware that both Greenland and the Faroe islands are not members of either the EU or the Schengen Area.