If your son has been diagnosed with all of those disorders, he must have seen psychologists/psychiatrists for the diagnosis. They should be able to give you advice for treatment. Many of the behaviors that you describe are not uncommon for children with ADHD or ODD. Kids with those disorders can be extremely impulsive - their impulses win out over reason - so your son knows he shouldn't do something, does it anyway because of his lack of impulse control, then feels the need to hide what he did because he knows it is wrong. As frustrated as you are - he probably is as well. This isn't the lack of impulse control that is typical of a young child (and appropriate for their age) - it is much worse than that in some kids with ADHD.
What you describe during your school time with him is typical of his diagnoses as well - the avoidance & "forgetfulness" - not unusual with the disorders you've given. Kids who truly have ADHD have minds that are running a mile a minute - they are VERY easily distracted & - even though you've told him to get something very specific - it does not surprise me that he gets distracted while he is up getting it & comes back without the things requested. Again - not your typical distractability that most kids have - this is more than that - & out of their control.
You should seek advice, assistance, treatment now - before the preteen years hit! You may want to consider talking to the local school district because public schools (& I say this without knowing your reason for homeschooling, so I realize you may not want to pursue this for your own reasons) have many many resources for students like your son. They have counselors, school psychologists, reading specialists, even support for the classroom teachers teaching students with difficulties. They may be able to provide services for your son that you can't at home.
Kids like your son can be a challenge, but they can be very spirited & talented kids too. My husband is an adult with ADHD & doing quite well now - I'd say partially "thanks" to his ADHD!! It took him a while to get to this point, but he now knows how to manage his life to make his disorder work for him & not against him.