The rules on having Strike with the Thrown option mention having to retrieve or recharge something to re-use the ability in order for it to count as a Thrown Strike instead of a Blast. Could this include something like throwing chunks of debris or cars, or do you need something other than Thrown Strike or Blast to add bonus damage to such thrown debris?
I believe that in 2E you already add your strength bonus to thrown items - this is built into the system, and doesn't need a power.
If you really need to deal a lot of damage, but only rarely, you could always power stunt a blast off of a super-strength or strike (strength-based) power. The blast could be described as "Throwing a chunk of street, as hard as you can".
Don't worry so much about the description, worry more about the effect you are causing. Does your character regularly throw random items at foes? Build them a Blast with the Flaw: requires rubble, debris, or other similar items.
For more information, you can always look into Ultimate Power. Or, if your group isn't opposed, take a look at 3rd edition (aka DC Adventures) - the powers are done significantly differently, and it makes it much clearer what the effects are.
edit: I've dug through my archives and found my M&M 2E book to confirm. Yes, a power that does ranged damage by throwing debris (even up to cars) that is regularly used is best modeled as Blast. Use the Limited: requires ammunition flaw (-1 point, flat).
Strike is 1 point per rank, with Thrown being an additional 1 point (power feat). Blast is 2 points per rank. It just wouldn't make sense, from a game balance perspective, for you to be able to duplicate a power (ranged damage every turn) for half the points.
@Cobalt: If it were the primary method of attack, I'd probably go for them buying Blast with either a Flaw or a Drawback depending on frequency (rule of thumb is that a -1 Flaw should make your power unavailable at least 50% of the time. Power Loss is more along the lines of every few encounters, you might be stuck without anything to pick up). Alternately, I'd just suggest that they buy up their Strength and/or build it as a "naked" Extra like with Throwing Mastery where it boosts the damage from something that normally would be harmless. If a player seems to be taking advantage of the improvised weapons, I'd either start having fewer available in the environment or start introducing plot complications where the city serves him with a lawsuit for the number of parking meters, buses, etc he's picked up to use as a weapon.