First, moving all of that junk into space at all is a huge amount of effort.
From some research, it seems that America lone throws away 300,000,000,000,000 lbs (300 trillion) of garbage each year. Sending anything into orbit to the ISS costs $10,000 per pound. It would cost 3 quadrillions just to get it all into orbit, setting aside practical issues like not even having the infrastructure and suitable technology to do it, nor there not being enough rocket fuel in the world to pull it off. Even if we somehow get it down to 1 cent per lb, that's 3 trillion dollars to get it all to space, every year.
The garbage when thrown towards orbit, will start orbiting Earth and hence creating a ring-like structure as shown in the conceptual image below.
Just to space; if we want to get it out of orbit (hint: we don't want it in orbit) it would cost even more. Getting it to a black hole adds many orders of magnitude to the difficulty. There is no point in that either.
Plus, it's not even desirable. Yes, we need to handle our trash better, but there is a lot of useful raw materials there. Biodegradable stuff is better used for compost and fertilizer. Other stuff should be recycled. Even if it's not worth recycling now, the economy may shift such that reclaiming old resources from the dumps is profitable, through some combination of making new materials costing more and recycling costing less.
The End Notes
It is possible, but not financially achievable. It would a lot more economical to just spill it into the molten heart of the Earth. However, as Daniel Spector wrote in his answer, it would be very wasteful to just dispose of our trash. Simply raising the global recycling efforts would be a much better solution.
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