8/11/2016 - Strain is a variation of evoke I hit on while working on motivated.You can get an effect, or a creature, or pay more for both. (Where with evoke you get an effect or pay more to get a creature too.)
It's sort of coincidence that all the strain costs are two mana. The trick with costing these is that the base mana cost is what you're paying to get the creature or the effect, so it has to be appropriate for each, while the strain cost plus the base mana cost is what you pay for both together. For small-medium creatures, most creatures and effects are going to be worth a bit more than a card, but the combined cost gets us into discount territory, hence strain costing 2.
To prove it's not a requirement, here are some cards where the strain cost isn't 2:
But it was hard work to find those. 2 is a shockingly natural place for the strain cost. Which is an argument for settling on that price and making it a keyword:
You could put strain on any permanent:
(Though I wouldn't really recommend it on lands.)
Demonstrating Jack's suggestion: