there isn't enough work for everyone

Immigrants induce demand for goods and services just like anyone else, thus the jobs to render those goods and services.

the crime just gets higher and higher

Technically depends on the country but this is usually false.

plus they do it illegally

Law is not morality. Perhaps it shouldn't be illegal.

Immigrants induce demand for goods and services, thus jobs

Except when the highest demand is for land. So they end up illegally occupying land, often government-maintained land.

Perhaps it shouldn't be illegal

If you're a third world country with a dense population and the population overflow is coming from an even more densely populated country that seems to have no motive to control it, then it damn right should be illegal. I'm not sacrificing my demographic if you can't take any right steps to regulate yours.

First of all, migrants not only generate jobs, but they also work the jobs that most native people don't want. Most farms and construction works nowadays are occupied by inmigrants, because they don't steal your job, they take the ones that you didn't like.

Second of all, most countries are not populated to their fullest. There's a lot of space, both horizontal and vertical, and Europe can perfectly house the inmigrants that it gets. And if space is such a big problem, then you should look at why we are letting entities like banks and "governments" have lots (thousands) of empty houses.