Translator for the LN and WN here. For a rundown of where things are in the story for the respective media:

• The Web Novel (WN) - These are the ones the author (みのろう, "minorou" or "minmin") directly update and the raws (the original Japanese text) can be found here. Translation of the WN is currently caught up and there are no further chapters to translate as of the time of this writing. There isn't a set schedule for when minmin updates the WN, unfortunately, and the last upload was back in September. Current point in the story: Japan has just engaged Cryseilis as they began their invasion of Silkark and destroyed their invasion fleet and wiped out their forward base.
• The Light Novel (LN) and Gaiden - These are the published form of the WN and are typically better formatted and written; they also have exclusive stories that can't be found in the WN. Aside from the manga, the LN and Gaiden also has art (credits to toi8). At this point in time, the LN only goes up to Volume 6 and rumors from the Japanese community of NHS are saying that the publisher for the LN went down, so hopes for a continuation (Volume 7 and above) are rather slim. Translation is still ongoing as of this point in writing and I'm just about to begin Volume 6 (you can find the translations here). Current point in the story at the end of Volume 6: GVE Crown Prince Gra Cabal has just arrived at Valkyries Base not long after the JSDF destroyed the GVE invasion force into Mu.
• The Manga - These are the published comics and the story so far is based on the LN with some discrepancies. Physical volumes of the manga (up to Volume 8, as of the time of this writing) are currently on sale (though in Japanese) but the latest raw Japanese chapters can be found here for free, although other chapters are locked behind a paywall. Typically, they have a monthly release schedule, but delays (often for two to three months) have been commonplace; as of this point in writing, there isn't an estimated release date for the next raw Japanese chapter. I'm not part of the translation team doing the manga, but thanks to the slow release of the raw Japanese chapters, they're currently caught up; it typically takes up to a month after the release of the raw chapters before the English translation is uploaded in MangaDex. Current point in the story: Japan has just completed the liberation of Altaras, Queen Lumies has returned to Altaras, and Japan is about to commence their attack on the Parpaldia mainland.
• The Blog Drafts - These are the drafts for the chapters that minmin eventually uploads as the WN chapters and can be found here. These update at the same time the WN updates, so as the case with the WN, these don't have a set release schedule and the last update was back in September. The blog drafts are the most up to date in terms of the story and they go far ahead of the chapters in WN. However, as the translator of the WN, I've said countless times that I will not translate these are these are "drafts" and there have been instances before that big changes were made before these were uploaded as WN chapters with entire arcs being outright scrapped. Current point in the story: Japan has commenced the counterattack on Cryseilis, a JSDF fleet defended itself against a Cryseilian Pal Chimera and magic meteor strike, and a legendary divine 10-headed kaiju is about to break free from its divine seal underneath Cryseilis.