Any court from a municipal traffic court on up can declare a law unconstitutional and the U.S. Supreme Court is almost never the court that does so in the first instance.
Also, while the jurisdiction stripping law that you suggest might be unconstitutional, it is not obviously unconstitutional. The relevant language is in Article III, Section 2 of the United States Constitution (this has been modified by the 11th Amendment in ways that are not pertinent to the issue at hand):
The judicial Power shall extend to all Cases, in Law and Equity,
arising under this Constitution, the Laws of the United States, and
Treaties made, or which shall be made, under their Authority;--to all
Cases affecting Ambassadors, other public Ministers and Consuls;--to
all Cases of admiralty and maritime Jurisdiction;--to Controversies to
which the United States shall be a Party;-- to Controversies between
two or more States;--between a State and Citizens of another
State;--between Citizens of different States;--between Citizens of the
same State claiming Lands under Grants of different States, and
between a State, or the Citizens thereof, and foreign States, Citizens
In all Cases affecting Ambassadors, other public Ministers and
Consuls, and those in which a State shall be Party, the supreme Court
shall have original Jurisdiction. In all the other Cases before
mentioned, the supreme Court shall have appellate Jurisdiction, both
as to Law and Fact, with such Exceptions, and under such Regulations
as the Congress shall make.
The key language being the language in bold, who scope and limitations are the subject of hot debate in legal scholarship.
For example, both military tribunal law for non-soldiers and the collateral review of death sentences implicate this provision. An issue related to U.S. Supreme Court jurisdiction over military court-martial court composition will be heard this year in oral argument before the U.S. Supreme Court.
There is also debate over whether the jurisdiction of every single federal court can be removed from a matter within the judicial power of the United States.
In that regard, keep in mind that the United States federal court system did not have direct appeals of criminal convictions at all until the 1890s, although you could challenge, for example, the jurisdiction of a criminal court over your case with a writ of habeas corpus which is a collateral attack on a conviction in a separate civil lawsuit formally directed at your prison warden.
That being said, as far as I know, a law is considered in effect until
declared unconstitutional. It is illegal to break an unconstitutional
law, until declared so.
You are wrong. A law that is unconstitutional on its face is, in terms of legal theory, unconstitutional immediately upon enactment and a court simply acknowledges that fact. It is not illegal to break an unconstitutional law even if no court has yet declared it to be unconstitutional (in U.S. jurisprudence). A law that is unconstitutional as applied is unconstitutional in application at the moment it is applied unconstitutionally, and again, a court merely acknowledges that fact.