The National Rifle Association doesn’t shoot straight when it comes to documenting its lobbying and political activities, filing tax forms for years that were littered with information gaps and apparent falsehoods, a Post review of the filings found.

The NRA, which was founded in New York in 1871 and claims to have millions of members, even told the IRS it didn’t receive membership dues, thus enabling it to avoid disclosing more about its activities. Last year, it spent $345 million.

And for six years on tax filings, the NRA failed to list the Political Victory Fund, its PAC, as one of its associated organizations. These tax documents are signed under “penalties of perjury.”

“How that form wasn’t intended to mislead the IRS, I don’t know. I don’t know how you come to any other conclusion,” said lawyer Marcus Owens, a former IRS official and leading expert on non-profit tax law.

In fact, the $10 million Political Victory Fund suddenly appeared after a six-year absence on the NRA’s 2014 filings, forms that only recently became public. That change, and a few more, came only after scathing press reports and calls for federal investigations.

For seven years, the NRA also skipped a key question on its tax form — whether or not it engaged in lobbying. Asked to answer “yes” or “no,” it simply left the space blank.

The omission is strange for the powerful gun-rights advocacy group: the lobbyists it hires file official forms with Congress about their activities and spending.

Asked to detail expenses on its tax form, the NRA told the IRS it spent nothing on lobbying each year from 2008 to 2013.

In 2014, it finally recorded $1 million in lobbying expenses. But even that figure is at odds with the amount reported to Congress of $3.4 million, according to data on the OpenSecrets Web site.

It also recorded spending $23 million on unspecified “legislative programs.”

In 2014, the NRA for the first time acknowledged that it receives membership dues, which start at $35 a year. Its latest tax filing show it took in $310 million last year, including $128 million in membership dues.

The organization doesn’t disclose how much of the total came from corporate members like gun manufacturers and how much from individual supporters.

It also answered “yes” in 2014 filings to whether it conducted political activity — something the NRA denied in its previous six IRS filings. Such activity is potentially subject to tax. The NRA reported paying $1.6 million in taxes last year on its political activity.

When a Yahoo news story earlier this year exposed the previous omissions, the NRA said it paid all relevant taxes and blamed the reporting lapses on a “clerical error.”

But a watchdog group wasn’t buying that explanation.

“The NRA is a sophisticated entity that only filed its tax returns after multiple layers of internal and external review, making it difficult to believe a clerical error is responsible for the NRA’s failure to report its political expenditures for at least six years,” wrote Noah Bookbinder of Citizens for Responsibility and Ethics in Washington in a June 2015 letter to the IRS.

CREW also asked the Federal Elections Commission to audit the NRA. The FEC wouldn’t comment, but a recent filing on its Web site shows the NRA paid the agency $2,750 as part of a settlement agreement.

New York Attorney General Eric Schneiderman’s office, which regulates nonprofits and collects both the federal tax return and audited financial statements from the NRA, refused to comment on whether it was investigating the organization.