I'm a little confused about the EDF games storywise. Is Global Defence Force, Earth Defence Force 2017, Earth Defence Force - Insect Armageddon, etc. stand alone or are they connected storywise?
The EDF games barely have a story at all. People shoot alien bugs is about it.
EDF 2017 starts with human's first contact with aliens (including a great "We're calling them Ravagers. We hope they're friendly" bit), followed by them invading in 2017. Seeing as how you fight aliens in the previous games, it's obviously not a direct sequel.
Global Defence Force is the original set of games, however with EDF 2017 we get a bit of a "reboot".
Earth Defence Force 2017 begins with first contact (detected in 2013).
Earth Defence Force: Insect Armageddon happens at the same time in "New Detroit".
Earth Defence Force 2025 refers often to events "seven years ago" which is referring to 2017/IA. The adventures of a "hero" are mentioned (the commander mentions it a couple of times, working with him, as do the soldiers on the ground occasionally (in disbelief)). This could be either Storm1 or Lightning Alpha (though likely the former as 2025 is set in Japan as was 2017, and in IA the commander appears to have some superiors and be at odds with them (listen to the final level's voice acting)).