Their objective would be to enslave, or repopulate their species or relocate.
Yeah, the distinction between which of those three REALLY makes a difference. If it's the first, making us cost more through attrition, terrorism, and wonton destruction then we are worth on alien slave-and-or-meat markets might work.
Repopulation might have some interesting options, but it is again to vague. The morbid, but effective, question I want to know is... do the aliens value the life of their offspring??
But if they are here to relocate, then fighting them and making us "not worth the effort" of conquest is likely a really
bad idea. Since these aliens have the option of: forcibly settle earth or die, they will fight to the death.
The distinction between the first motive and third motive literally turns a good idea into a terrible one, which is why I again think we need more information before we can answer.
But I'd assume they'd be pretty tough if they can do what we can't do.
Fair assumption.
Fortunately there'd be more of us than them
Weird and completely baseless assumption. Occasionally the conquerors can outnumber the natives. Imagine a large empire with a large military conquering a tiny island with a small tribe on it. In that case, the invaders could very well outnumber the islanders. Now swap out the word "island" for "planet".
and we have the home field advantage.
Again fair assumption.
How would they invade? Well, with ships of course, unless they bring troops through a dimensional portal of some kind.
Not what I meant as in "how". If the aliens don't need our food, they might target our farmlands to starve us out, or they want our farmlands and try to capture them and not destroy. The same is true for any of our natural resources. Perhaps they could use our oil. Perhaps they have no need for it and thus target the resource to cripple us.
They might try for "shock-and-awe" style tactics and target civilians in order to scare us into surrender. Then again, these aliens might have a religion that limits what they are allowed to do in warfare, similar to Islam, and might find it unholy or evil to target noncombatants. Or they might have some sort of Cosmic United Nations equivalent preventing them from using chemical weapons against us, or other classes of weapons.
They might target our military first, or they might target our economy first in order to cripple the military.
They might come in through brute force, or they may try to invade by political subversion and manipulation. It could either be
War of the Worlds or
They Live depending on anything.
They might wage their campaign of conquest in the open, or they may be fans of espionage and covert warfare.
They might be motivated by greed, in which case they'll fight conservatively and carefully, not risking expenses, or they might be motivated by ideology, in which case they may fight to the death.
They might be united in their motives to conquer us, or there may be aliens within their society sympathetic to us and willing to help us.
All of these factors, and
more decisively affect what the best way to counter the alien threat is. Currently, I don't have enough information to say what the best strategy would be.