Legally speaking, the USSR was a voluntary union of 15 constitute republics, who agreed to a Supreme Soviet to direct them in certain matters. That is at least according to article 4 of the 1924 version of the USSR's constitution (article's 1 and 3 outlined the powers of the Supreme Soviet and the individual republics), and further confirmed in the two subsequent constitutions: the 1936 "Stalin Constitution" (article 17 allowed any republic to leave, while 14 confirmed duties of the Supreme Soviet, and 16 confirmed each republic had its own constitution), and the 1977 version (article 72 allowed them to leave).

Obviously that is simply not how it worked in the USSR, as evident when republics actually did try to leave; though there are many example to choose from, I'll cite the example of Georgia in 1991: they actually cited article 26 of the 1922 Union Treaty that formed the USSR (which again, allowed the right to withdraw from the Union) as a case to leave, though obviously that didn't have any meaning to anyone in the USSR. In effect once part of the USSR, republics were bound there until the end.

I would say that because it did have overreaching laws that effected each republic, but also allowed those republics some degree of autonomy (especially with the rise of Gorbachev and his policies) I would say that it was more like the US than the EU, except each republic was far more nationalised, much like the EU.

It was a nation in which USSR law applied to all 15 members, unlike the EU in which law varies by country. It also had a collective military and planned economy, the EU retains separate militaries (basically), but they do have an integrated market economy.

Basically, no. The USSR was a nation, the EU is a confederation.