The Hague conventions of 1907 do not prohibit big bullets , but it does set limits on what you can do and subject to interpretation of parties at hand and after the fact.
As you can see below a case could be made against the 50 cal and anti aircraft type weapons being employed in an anti personnel role.
Article 22
The right of belligerents to adopt means of injuring the enemy is not unlimited.
Article 23
Besides the prohibitions provided by special Conventions, it is especially prohibited:--
To employ poison or poisoned arms;
To kill or wound treacherously individuals belonging to the hostile nation or army;
To kill or wound an enemy who, having laid down arms, or having no longer means of defence, has surrendered at discretion;
To declare that no quarter will be given;
"To employ arms, projectiles, or material of a nature to cause superfluous injury; "
To make improper use of a flag of truce, the national flag, or military ensigns and the enemy's uniform, as well as the distinctive badges of the Geneva Convention;
To destroy or seize the enemy's property, unless such destruction or seizure be imperatively demanded by the necessities of war.
If a combatant were to be captured and it could be shown that he employed " arms, projectile, or material of a nature to cause a superflous injury" then the country could conceivably try him/her/them as a war criminal.
BUT both parties have to be signatories to the accord and also declare war as per the rules of the accord.
Vietnam was a police action, not a war in the strictess intepretation of war under International Law.
Gulf War 1 and 2 are also police actions, since they are basically covered by the various UN resolutions .
The War on Terror is also not a formalised war as per the Hague Conventions or International Law.
So really the 4 cases above are not really limited by the Hague accords and it basically means anything goes with the only limiting factors being treaties concerning the use and implementation of Chemical, Nuclear, and Biological agents and some other recognized standards as laid out under International Law.
I should also note that the United States Never ratified the Hague Conventions of 1907 and therefore are not bound by them, but have observed the letter of the accord since it's acceptance.