Can I enter the US under the VWP as a Dutch and Iranian national?

You will need to apply for a visa.

This text is taken directly from this page on the US CBP web site (my emphasis):

Travelers in the following categories are no longer eligible to travel or be admitted to the United States under the Visa Waiver Program (VWP):

• Nationals of VWP countries who have traveled to or been present in Iran, Iraq, North Korea, Sudan, Syria, Libya, Somalia and Yemen on or after March 1, 2011 (with limited exceptions for travel for diplomatic or military purposes in the service of a VWP country).
• Nationals of VWP countries who are also nationals of Iran, Iraq, North Korea, Sudan, or Syria.

No, you need a visa. Apply for a B1/B2 visa on your Dutch passport, and if asked at the interview why you want a visa, explain it's because you're a dual Iranian national.

Bring (on paper) solid evidence of financial capacity and ties to the country where you live (marriage certificate, childrens' birth certificate, proof of income, consecutive bank statements, property ownership proof, notarised employment letter...) and answer any and all questions confidently and truthfully, even if you feel they're personal and invasive.

The fact is, anecdotal evidence suggests that, for those dual nationals who (correctly) apply for a visa, many consular officers will dig for reasons to deny a visa, as they're meant to represent US foreign policy to some extent, with which the relevant countries evidently haven't been currying much favour as of late. That's why you should be careful to bring any and all documentation available to you. You may not be asked a lot, in which case all good, but don't take any chances, as a refusal, despite what the letter states, will make it harder to get a visa in the future.

No, you may not visit the USA without a visa.

Nationals of certain countries, including the Netherlands, may visit the USA under the Visa Waiver Program. Several conditions must be met, including not also being a national of Iran.

While this does not fully answer your question, please note that as the case of Annahita Mazaheri demonstrates, even with a visa you may still not be allowed to visit the USA. I don't know what you can do to prevent the following from happening, just be mentally prepared.

Annahita Mazaheri is a Dutch woman born of Iranian parents. She hadn't been to Iran for over 17 years and had a valid visa for the USA, but was turned down at the gate after a short interview with US officials (on Dutch soil) in early January 2020.

And yet the impossible happened. At the last passport check before boarding, the stewardess suddenly recalled Annahita with the announcement that the US immigration service was on its way. Three men in suits appeared shortly. She had to sit at the gate and was subjected to a rapid fire of questions. "They were just questions such as where I come from and what I do in daily life. Nothing crazy. The whole time I thought I could walk on to the plane just like that," Annahita reflects.

_{—"Annahita krijgt duizenden reacties nadat ze op vlucht naar VS wordt geweigerd" (in Dutch), Het Parool, 2020-01-10 (translated from article)}

As can be read in an article on Dutch News on the same incident, Stef Blok —the Dutch minister of Foreign Affairs— has been asked by parliament to explain why Annahita Mazaheri was barred from flying to the US, and what authority US immigration service officials have on Dutch soil.

The exact questions asked are available online (in Dutch). They show that Ankie Broekers-Knol —the Dutch state secretary for Immigration, within the department of Justice and Security— was asked questions as well. One of the questions identifies the men as US Immigration Liaison Officers.

As it transpires, Annahita had applied for an ESTA instead of a visa, for which she may not have been eligible.

Reaction American Airlines and Customs and Border Protection

American Airlines has confirmed that Annahita was refused on a flight from Schiphol to Philadelphia. A spokeswoman of American Airlines told NH Nieuws that she cannot provide any explanation for the refusal of Annahita, because the decision was made by the American Customs and Border Protection, which the airline has to follow.

Custom and Border Protection says that Annahita's background has nothing to do with the refusal. Instead of an Esta, she should have applied for a Non-immigrant visa.

_{—"Annahita (22) beleeft nachtmerrie: 'Geweigerd voor vlucht vanwege Iraanse afkomst'" (in Dutch), NH Nieuws, 2020-01-10 (translated from article)}

It's a tough time for people with Iranian connections to enter the U.S. There are news reports here in Canada of Iranian-born people with Canadian and even American citizenship being detained for hours and questioned at land border crossings. https://www.cbc.ca/news/canada/british-columbia/iranian-canadians-detained-interrogated-at-us-border-1.5415782)