Why won't my plugs stay put in concrete wall?
If they are coming out when you are tightening them, it might be that your hole was not drilled deep enough.  The hole should be at least 1/4" deeper than the screw.

Those plugs also might not be large enough for the job.  Concrete anchor scews (like Tapcon's) are a good alternative when you need more strength then a plug can offer, but don't need a large metal anchor.  On large jobs (like attaching a deck to the house), you can epoxy a bolt in a hole like you suggsted.