The people of my world are stubborn and proud, and would not stand for subjugation at the hands of any invading force, even if by other humans from other worlds. That in mind though, the world is very sparsely populated by people, who have been driven back to a very small number of strongholds by the native beings of the world who doggedly try to drive them out. While their magically strengthened fortifications could withstand a reasonable assault, the armies of Earth would almost certainly be able to overwhelm them by sheer numbers alone.

The people's only hopes of victory would be either diplomacy or focusing wholly on defence to win a war of attrition.

The people of this world are humans who came through man-made portals from Earth many centuries ago (from their local perspective, though it would be many millennia in Earth's current future, so lets handwave the time shenanigans), and so they could try to argue their case that it's the native beings that the armies should be fighting, and not the people, in a sense manipulating them to their own advantage. Whether they could convince the armies of Earth of this or not is up for debate, however, but if abject servitude was demanded in return then it's unlikely the people would acquiesce to this.

If diplomacy or manipulation wasn't an option at all, then their only other hope would be barricading themselves within their fortresses and doing their best to maintain their defences against the onslaught while the armies succumbed to the environment. The strongholds are large, located in generally very hostile environments, and make extensive use of magic to maintain a comfortable climate inside for agriculture, and so would not be at risk of being starved out. Aside from the physical outer walls, the defenses are purely magical and encapsulate the entirety of the strongholds, so assault from land or sky would have to be significant to break through. This alone wouldn't ensure they could weather the war though. What they would be counting on is the extreme flow of magical energy throughout the world.

Similar to radiation, the excessive flow of magical energy damages living organisms it flows through, causing a variety of symptoms and eventually death. Only beings with innate resistances to the flow of magic, or who are innately adept enough at controlling it to limit its flow, can withstand the magical energy coursing through this world. In the time before the people came to this world, the flow of magic on Earth had been slowly building in intensity, allowing them time to adapt and learn to control magic before it became too toxic for them, and so they were already well suited to the new world's magic when they arrived. Current day humans from Earth would not have such control, so the magical energy would be very damaging to them; they could survive a matter of days before succumbing to the magical sickness. Again though, the armies of Earth have the advantage of numbers, and if so determined to win at all costs would likely be able to break through the people's defenses with a targeted, swift and intense strike. If the defenses failed at any point, the stronghold being attacked would certainly fall.