If you strip away all the misdirection, the airline's denial can be paraphrased as:

An inspection was conducted. The aircraft passed the inspection.

and

This was an extraordinary circumstance.

If for this airline, having its planes pass inspections without finding failures is extraordinary, that surely is not a fact they should like to advertise.

I think you will win your claim easily if you point out that passing an inspection can be extraordinary only if the airline ordinarily fails inspections.

IANAL, but my understanding of the situation is that they're using some really selective and literal reading of the van der Lans judgment to try to make you go away. As the EU website on passenger rights suggests, it's probably a good time to complain to the relevant national authority. They should then advise you on how to proceed further.

The ruling in Case C?257/14 (van der Lans vs KLM) contains the following paragraphs that I feel are the most relevant (emphasis mine everywhere).

37. Since the functioning of aircraft inevitably gives rise to technical problems, air carriers are confronted as a matter of course in the exercise of their activity with such problems. In that connection, technical problems which come to light during maintenance of aircraft or on account of failure to carry out such maintenance cannot constitute, in themselves, ‘extraordinary circumstances’ under Article 5(3) of Regulation No 261/2004 …

Then there's an example of what would be an extraordinary technical issue, namely a fleet-wide defect:

38. Nevertheless, certain technical problems may constitute extraordinary circumstances. That would be the case in the situation where it was revealed by the manufacturer of the aircraft comprising the fleet of the air carrier concerned, or by a competent authority, that those aircraft, although already in service, are affected by a hidden manufacturing defect which impinges on flight safety. The same would hold for damage to aircraft caused by acts of sabotage or terrorism …

The ruling also clarifies that no matter how unexpected, technical issues are the airline's problem:

41. Next, it must be observed, first, that it is true that a breakdown, such as that at issue in the main proceedings, caused by the premature malfunction of certain components of an aircraft, constitutes an unexpected event. Nevertheless, such a breakdown remains intrinsically linked to the very complex operating system of the aircraft, which is operated by the air carrier in conditions, particularly meteorological conditions, which are often difficult or even extreme, it being understood moreover that no component of an aircraft lasts forever.

42. Therefore, it must be held that, in the course of the activities of an air carrier, that unexpected event is inherent in the normal exercise of an air carrier’s activity, as air carriers are confronted as a matter of course with unexpected technical problems.

Then, finally, comes the hammer that Norwegian is presently using to bash you:

43. Second, the prevention of such a breakdown or the repairs occasioned by it, including the replacement of a prematurely defective component, is not beyond the actual control of that carrier, since the latter is required to ensure the maintenance and proper functioning of the aircraft it operates for the purposes of its business.

So they're taking the bit about "including the replacement of components" as a restrictive clause, while my understanding is that the intended meaning is to expand and clarify the meaning of "repairs". Either way, whatever checks they did on your plane were probably conducted to "prevent a breakdown" and "ensure proper functioning", so the "extraordinary circumstances" exception shouldn't apply. Paragraph 35 suggests that this exception should only be applied in, let's say, extraordinary situations.

35. Next, it should be recalled that the Court has stated that, since it constitutes a derogation from the principle that passengers have the right to compensation, Article 5(3) must be interpreted strictly …

Airlines routinely attempt to get out of their payments, and attempting to make people go away with a form letter, even if it is completely fabricated nonsense, is so cheap that you can count on them trying. Heck, if one or two people go away after such a letter, it has already paid for itself.

I used to be a frequent flyer and I've had my share of delays, and by my experience the airline will almost always try to make you go away. A letter from a lawyer will shut them up and make them pay, so if you have a legal insurance that covers you, stop wasting your time and get them a letter from a lawyer.

I have never had to go to court, but my lawyers had to threaten court and prepare court papers more than once before the airline finally coughed up what nobody except them ever doubted they had to.

That being said in general, the exceptions provided in the law do not cover your case. Most importantly, exceptional circumstances are generally ruled as those outside of the control of the airline. Think erupting volcano, large-scale disaster or the destination airport being bombed (that, sadly, did actually happen to me).

Deciding to do an inspection of their own aircraft is definitely a decision that the airline made within its own sphere of control. At that point, it doesn't matter if they find something or not.

So, tl;dr:

if ($have_legal_insurance) haveLawyerSendLetter($airline)
else loop answerYourselfAndPersistInDemand($airline) until $they_paid
or giveCaseToOnlineCollectionAgency($yourchoice)

Yes, this happens so often that there are websites that you can sell your claim to and they will pay you upwards of 60% of your claim immediately, then pursue the case for you - which tells you that the airlines will eventually pay them in 80%+ of the cases.

It is very unfortunate that the airlines are refusing the compensation by using different tricks.

The case will be finalized as soon as we have received all the necessary information.

So please don`t give your bank information to the airline because in that case you are accepting the offer they have made to you i.e. you are accepting NOK 418.

Airplanes have very complex electronics. A pilot has to go through a pregiven preflight checklist i.e. that everything is working fine. If there is an error then he/she has to take countermeasures. So the airlines are required to carry out regular maintenances to avoid such errors/defects.

Where as a defect can be an exceptional circumstance but it very seldom. Despite that your airline has still not told you the exact technical fault in the email. Even a failure of hydraulics, fuel system, gasoline pump etc. are not exceptional circumstances. A list of such faults which are not exceptional circumstance including court decisions can be found here. (use translator)

So please ask the airline the exact technical fault and consult a laywer who is specialised in this area.

The most effective path of action may be to delegate your claim to specialized agencies. They know all the tricks used by air companies to refuse compensation, they have access to flight databases which list real causes of delays, they fully know EU261 and can launch legal action if needed. In exchange they pay themselves on a percentage (about 30%) of what they can get from air companies.

I would argue the following basis , and ignore completely the case they quote (which has been addressed in other answers):

The airline has claimed that it undertook an inspection, but that the fact nothing was in fact found to be wrong, causes this to be exceptional and outside their control.

However, a responsible proactive safety conscious airline, will always err on the side of caution. Therefore if in doubt they will check in depth, even if nothing is eventually found, because this is good safety practice.

As a result, a proportion of suspected issues will always turn out not to actually show a fault, AND, this reflects normal consequences of a diligent proactive and risk avoidant approach to safety. Being an expected event (however uncommon) that results from proper safety practices, it does not represent, and cannot be, either exceptional, or outside the control of the airline, in the sense that is required by governing law.

tl;dr - please don't fabricate fallacious reasons not to follow the law, and pay my costs in full.

In my complaints to the The Norwegian Travel Complaint Handling Body, and the EU Online Disputes Resolution, how should I most effectively argue against this logic?

I don't see that any logic has been presented. Their letter can be boiled down to two things:

(1) The departure was allegedly due to exceptional circumstances.

(2) There was a court case that addressed a highly specific circumstance that doesn't apply here.

For the first, they don't explicitly present an argument, but apparently they are claiming that inspection are exceptional, which is absurd. The second is denying the antecedent.

Are they correct that this "inspection that found nothing" constitutes exceptional circumstances?

How can something that happens every day be exceptional?