Can I connect a 1-3 adapter to a 12/3 extension cord?
So long as the total draw of all devices plugged in remains below the amp capacity of the power strip, the extension cord, the permanent wiring, and the breaker, you'll be fine.
I believe the admonition against plugging in a power strip is that

You are not allowed (by NEC) to use an extension cord for permanent wiring. i.e. if you need an outlet on the other side of the room for your entertainment center, you should have one wired in, don't run a cord across the floor, around the walls, (especially under a carpet!), whatever, to provide more-or-less permanent power to another location.
A power strip will allow you to plug multiple items in at the same time, greatly increasing the chance of overloading the circuit. If you plug in your miter saw, table saw and router into the power strip and you've got 3 people, each using a tool, you'll very quickly overload the circuity. The breaker will pop, but you could cause damage to the strip and/or extension cord before it does.

If you're using the extension cord as the only supply of power to the shed, and you're planning on leaving it plugged in all the time, that would (I believe) constitute a permanent installation and is banned.
Most importantly, if the cord is stretched across the lawn from the house into the shed, it'll be in the way of the lawn mower. It doesn't take much imagination to figure out what could go wrong there.
If you roll out the extension cord to plug in a fan and a radio while you're out in the shed gardening, then you roll it back up and put it away at the end of the day, then you shouldn't have any issues with the extension cord or with the temporary use of a power strip (to enable plugging in two reasonably low power devices).