What would be the easiest way to make an image copy of an internal HDD to an external USB one (HDD) without any installing of additional software? Image copy, as in, I wish to have a complete copy which I can boot it on another computer.
The Live CD GParted Live comes with the tool partimage. It allows you to create an image of a disk to another one and restore it afterwards.
I would suggest looking at Clonezilla Live. It makes use of partimage, dd and/or partclone and it can be used to duplicate partitions, as you require.
Also, since it is a Live CD (or USB) this can be done without writing anything to the source partition.