First of all, if you're a citizen of the EU, you don't need a visa to come to Canada. You only need a permit to work in Canada.
Yes, it is possible and (as far as I know) legal to apply for both IEC and Express Entry at the same time. But mkennedy is right, Express Entry is only the first step toward Permanent Residency (PR) and getting PR might take a while (even though CIC recently said they want to process applications in six months or less).
You might want to consider coming to Canada on an IEC, then finding a job as soon as possible, and applying for a temporary Work Permit, so you can stay and work for another 2 years. That would give you enough time to apply for PR. Note that applying for a Work Permit can take some time too, since your company might have to get a Labour Market Impact Assessment (LMIA) to prove that you're not taking away jobs from Canadians. This can take a couple months. (I speak from experience.) Once you have the LMIA, you could speed things up by going to a Port of Entry (i.e. the border) and applying for a Work Permit there. Then they will process your application immediately and you will have a decision within an hour or so. (Again, I speak from experience.) Also note that the Work Permit may be limited to the employer who got you the LMIA, so you might not be allowed to change jobs until you get PR.
Another option is to come to Canada on an IEC, find a permanent job, apply through Express Entry, get an Invitation to Apply, actually apply for PR, and while you're application is being processed, you can apply for a Bridging Open Work Permit (BOWP). The BOWP allows you to stay in Canada and keep working until your PR application has been decided. This option is a little less safe because it is not entirely clear whether your PR application must have passed the completeness check before you can apply for a BOWP. My immigration lawyer said different CIC officers handle this differently. And it seems that CIC has recently decided to speed up the PR application process by postponing the completeness check until they make the final decision on the application. So, the completeness check might only be done when your PR application is receiving its final decision, but the completeness check might be required to get a BOWP, which you would need before you are granted PR. (Yes, this would lead to a contradiction.)