What might be a good strategy for an infrequent IHG user? I stay at an IHG hotel anywhere from 0 to 6 nights per year. I only earn points from hotel stays, not a credit card.

Strategy 1: earn airline miles for stays. Might earn 150-200 miles per stay. Don't have to worry about IHG point expiring.

Strategy 2: earn IHG points. Sometimes can earn more if there is a low season or winter promotion. risk of points expiring. Might earn 1000 to 2000 points per stay so zero to 1000 to 8000 points per year. Maybe redeem for a hotel stay every 3-4 years.

Math:
1 stay - 200 airline miles versus 1000 IGH points
10 stays - 2000 airline miles versus 10,000 to 12,000 points
20 stays - 4000 airline miles versus 20,000 to 25,000 points, $40-60 worth of airline points versus $125 hotel stay free

So IHG points are worth more if they don't become expired and you can redeem it for a room. Otherwise, airline mile are a safer bet. In contrast, Hilton Honors requires that you reach a certain level, possibly 10,000 Hilton Honors points before you can convert the points to miles. In Hilton's case, one has no choice. One must earn points and then, later on, decide to redeem it for airline miles (worse rate) or a hotel room (better redemption rate).

What do you think?

If you value airline loyalty and stay so little, you can use a travel portal such as Advantage Hotels (or your airline's portal) and get X number of miles for usually a similar price. It sounds like you have no status with IHG so it wouldn't matter anyhow. I have found AA hotels a decent way to pad my status boosting. 2000-5000 miles/Loyalty Points is far better. It is third party, of course, but in your case, unlikely to matter. UA, DL, Southwest etc. have them.

Also you could just get the IHG Premier Card for $99 a year, which includes a free night (so pays for itself). That gives you instant status.

Am I correct in assuming you are US-based (as you reference the dollar)? 1000-2000 points per night seems low to me considering US and the fact that IHG has a double point promo running most of the year.

You can also stop point expiry by buying a digital item (for 500 points or so) in IHG's store.

I'd take the IHG points and the IHG member rate over the abysmal mileage earning. It becomes even clearer if there is a corporate code you can use.

This. If OP is a free agent (no status in any hotel chain) then picking the hotel you want from a front offering miles (AA, Kaligo, rocketmiles [if it still exists]) or free nights (bookingcom, hotelscom) sounds the most sensible option.

I see little point in even having an IHG account for so little useage.

So be a free agent and book whatever hotel meets your needs in a particular destination.

Book via an OTA such as Expedia and collect their points as well as via a cash rebate site such as Top Cash Back.

Disagree. Of course, be a free agent with so little usage but even a single stay with a programme can sometimes be hugely profitable on its own. Have experienced it soon often with all kinds of loyalty programmes.. Expect to lose some points balances, but many single stays can be hugely worth it. Of course, you'll also find plenty cases where going OTA makes more sense. Just keep an open mind, though. I've saved or made hundreds of euros with one and done loyalty program usages.