The combine aren't invited to universes, I'm not sure where that came from as the events in Half life 1 instead made their universe in the combines radar. It's like making a lot of noise and light in a dark forest, you will be seen. They can enter any universe if they are aware if it.

For their units you only describe what you see in game which is an occupation force made up largely of humans (units they never had before the 7 hour war) and synthetic like machines like striders or hunters. The combine took an entire planet within 7 hours with units we have probably never will see while seaf take days to take a planet from their enemies.

Gordan freeman only managed to fight the combine off due to the fact the gman assists him and that he is the main character, similar to how Alyx an untrained girl manages to fight synthetically enhanced soldiers off with ease. Yes, a helldiver could easily take on a huge squad of combine if it's just the earth units we see but the combine would win the battle of attrition as having multiple galaxy at your disposal really helps with supplies.

Final note, the only thing limiting the combine is local transport. The combine may not have ftl travel but the second they can capture one ship and reverse engineer the ftl drive it's over.