Technically, nobody; the Constitution doesn't grant that power to anyone. The men who wrote the Constitution were largely idealists; to some extent, they neglected to include enforcement mechanisms in the Constitution to protect it.
The Supreme Court assumed this power for itself in the 1803 decision "Marbury vs Madison" and declared, in essence, that since nobody else had the power to declare bad laws unconstitutional, that the Supreme Court would do so.
For the first 150 years or so, this worked out well enough; the power of the Federal government was limited enough that the impact of bad laws was not widely felt. But since 1960 or so, more and more laws have become federalized, to the point that the States are entirely hamstrung by federal regulations. (The Constitution also does not allow Congress to delegate their lawmaking power to unelected bureaucrats and members of the Executive branch, but as I say, nobody much defends the Constitution any more.)
The judicial branch of the government (overseen ultimately by the Supreme Court) has the power to declare laws unconstitutional.
The Supreme Court
The federal courts can check the Presidents power by that courts can declare executive actions unconstitutional.
True
"The federal courts can check the Presidents How_can_Federal_Court_check_the_presidents_powerby that courts can declare executive actions unconstitutional."
Congress cannot declare laws unconstitutional. The Judiciary Branch may declare a law unconstitutional only if it conflicts with some provision of the State or Federal Constitution. The Supreme Court can rule a law to be unconstitutional, but Congress, along with the States, can only amend the Constitution.
The Judicial Branch has the power to declare the acts unconstitutional.
The Supreme Court gained the power to declare laws unconstitutional
The Judicial branch.
That power is the power of judicial review.
One Constitutional power specifically delegated to the federal government is the power to declare war.
The power to declare legislation to be unconstitutional and, therefore, unenforceable.
Can declare laws unconstitutional
judicial