This particular vote is non-binding, but the same is true about a lot of votes in national parliaments. You are also wrong to say that the Europarliament "[is] very weak and has limited influence"; actually it has equal power with the European Council over all EU legislation, and it has full veto pwer. For instance, MEPs rejected ACTA last year, meaning that the EU is unable to sign the treaty. It also rejected the software patents directive (remember that?) in 2005.
Also because of the principle of separation of powers, MEPs are independent of both the Council and the Commission: there is no "payroll vote" as in most national parliaments, and consequently party discipline is much weaker. The situation is similar to that of US Congress; a US President cannot bank on unqualified support from Congress even when both the House and Senate are controlled by his own party.
Finally the European Commission is indeed the executive branch of the EU, but it is NOT "directed by national governments": you are probably thinking of the Council, which is indeed made up of representatives of national governments. You can think of it as a kind of unelected Senate. Commissioners are appointed by national governments of each country, but once appointed they are independent of the government that appointed them.