Practically speaking, the answer is largely no: the closest things the United States does to election invalidation on a semi-regular basis are recall elections, a procedure that allows citizens to petition for a vote to remove and replace a public official before the end of a term of office. However, recall elections have largely been used to remove an official from office when his/her constituents think they aren't upholding the duties of their office, not as a measure of election invalidation due to election fraud or interference. Recalls are more the American equivalent of a vote of no confidence than a measure for election invalidation.

The Constitution provides no clear answer to the question (especially on the presidential level), as the heightened discussion around the 2016 election results will attest to. For the presidency, constitutionally speaking options are essentially limited to impeachment (which could be used to effectively invalidate an election as soon as the President takes the oath of office) and the cabinet holding a majority vote that the President is “unable to discharge the powers and duties of his office” (via the 25th Amendment). There's some lively debate on whether mass electoral college voter defection (which has never happened, but is theoretically possible) would be considered election nullification or not; it certainly wouldn't trigger a re-do election, which in my mind puts it squarely in the 'no it's not nullification/invalidation' camp. The closest equivalent on the presidential level that actually happened would be the 2000 Bush v. Gore election and the infamous Florida recount, when there was a huge legal battle over whether or not the results could be certified, including a protest by black lawmakers who wanted Congress to refuse to certify the results (citing mass disenfranchisement).

Legally speaking, refusal to certify (which is what's going on in North Carolina right now) is the closest thing we have to election invalidation; if the board of elections or local judge refuses to certify election results, they are legally not considered valid results. Each state's Secretary of State has to certify the results of any federal-level election, and Congress has to certify presidential election results.

It's fairly rare, but refusal to certify has happened (and almost happened) multiple times, mostly on the local and state level. For example, a local school board primary election was voided in Georgia in 2004 and a substitute election was ordered, and the results of a local judicial election were "put on hold" for over 18 months while litigation concerning the election results worked its way through the courts. The Illinois State Supreme Court ordered a do-over primary election back in 2002, but dropped it and ordered a hard recount instead. The argument of the appellate court was that a revote was an unnecessarily drastic measure to take to decide a close election, but did not argue the viability or legal possibility of a revote; a revote is thus theoretically possible (at least, in Illinois for state-level races).

I think the closest instance to election invalidation on the federal level is probably Senator William Lorimer (R-Illinois), whose election was declared invalid by the Senate due to bribery of electors after two successive investigations in 1910 and 1912.

The bottom line on election invalidation: it's exceedingly rare, but it does happen. However, under the law the US does not have the ability to "annul" an election on fraud grounds like many other countries do; there are certain steps you can take to remove someone who has committed illegal acts to attain their seat, including election fraud, once they have taken office, but there's no hard law allowing for annulment/invalidation until they're seated.