We installed a power strip with what we think is a 20 amp male connector -- there's the round ground plug, and two regular prongs, only one of them is veritcal and one horizontal.

We didn't notice this at time of purchase and just want to plug the power strip into a standard grounded home socket.

Can we buy an adapter to connect these two?

No, the item being used operates and needs a 20 amp circuit, so you will need to use 20 amp extensions and wiring.

And you most certainly don't want to use it in to a power strip.

It will need to be pluged into a 20 amp plug.
20 amp is standard in many homes.

If the 15 amp duplex you want to plug your strip into is on a 20 amp circuit then you can replace it with a 20 amp duplex. Other than that, your options are buy a 15 amp power strip or have a new circuit put in.

Just to clarify,

Simply replacing a 15 amp receptacle with a 20 amp receptacle is not allowed and a code violation without #12 wire and 20 amp breaker.

To answer the original, there is no adapter to allow a 20 amp device to be plugged into a 15 amp outlet.

Andrea, The smart thing to do is return the power strip and get a 15a power strip.