Soldiers and Military when following/executing orders, do you just do as you are told or do you consider the moral implications of things ?

In a live fire combat situation you do as ordered. After it is all over if you have concerns you bring them up to the person over the person who gave the order, to the JAG office or take it to a chaplain. If it is not a situation where a sudden response is required then you can question the order or even refuse to do it. In WW II there were a number of German soldiers who refused to work in the concentration camps. Nothing was ever done to them. When those tried at the Nuremberg trials tried to claim they were only following orders under threat of punishment if they did not, those Germans who did refuse orders were brought forward to show that there was no punishment for refusing to do as told in that situation.

soldiers have the right and the moral obligation to disobey   UNLAWFUL orders. 

If I was ordered to summarily execute prisoners in my charge....that is an UNLAWFUL order. 

I remember all too well the case of the soldier who REFUSED to don the Blue UN Beret,  arguing that it was an UNLAWFUL order,  and he did not JOIN the UN......he joined the US ARMY.......and a blue  UN Beret, was NOT part of the Army uniform . 

They attempted to court martial for insuborination,  but turned out , he was 100% correct.   So they burned him for something else, because he embarrassed the President,   Dumbya Bush at the time, for not knowing the REGS.  They nailed him for some petty BS  instead.  I contributed to his defense fund.  He was absolutely right.........but made a misstep in the way he went about protesting......so they got him on some trumped up BS. 

since WW2 we have introduced the words Sir is that a Lawful command Putting the Onus on the Officer making the Order

You have to obey a legal order.

All orders are assessed to make sure they are legal (they always have been in my 43 years of military service), and if they are, they are followed - period.

You follow orders, unless you know for certain it is an Illegal order.

--  That is the canundrum (unsure of spelling). Soldiers are taught and expected to obey orders at all times, but there is also the right, and expectation, that they can disobey "unlawful orders" or laws that are "crimes against humanity".  They can legally be prosecuted for carrying out "war crimes" and "Crimes against humanity" and the excuse of "obeying orders" is NOT accepted, as stated, and made part of international law, by the Nuremberg War Crimes Tribunal.

--  That is the problem -- they can be prosecuted, and even executed, for disobeying orders by a superior or they can be prosecuted for war crimes.