Sammy wrote

I like to keep my old bank cards intact and use them
for jobs around the house. My worry is that the data
on the magnetic strip can still be read.

That is only part of the problem, the other part is the
numbers embossed on the card. While the expiry date
would normally be obsolete, its often possible to guess
the new one that is on the card that replaced it.

So, while its easy enough to remove the magnetic stripe
and signature strip, its harder to get rid of the embossed
numbers and still have a useful bit of plastic.

What is the best way to destroy that data
without messing up the card for D-I-Y work.

Hard to say if you dont say what you use them for.

Does a domestic microwave detroy data on a magnetic strip?

Nope.

I tried using some of those strong magnets taken from a hard
drive. I put one above and one below the bank card and then
slowly drew the magnets along the magnetic strip. Is this enough?

Normally, but its hard to be sure that the data cant be
extracted by someone who cares enough to go to the
trouble. The card isnt much use without the pin tho.

Is it better to do this relatively quickly or relatively slowly?

Doesnt matter.

ISTR something about vertical and horizontal magnetic polarization
and maybe this is something I have to deal with in case it makes the
magnetic data harder to destroy???

Its better to just remove the entire magnetic stripe.

Is it better to scratch the magnetic strip with a sharp point?

Sandpaper is better or run it against an abrasive wheel
or wire brush on an angle grinder. Bit risky finger wise tho.