The rulebook states that in case of Battles, the Resolution abilities are resolves in the order the player wishes. However, in case of Sieges, it is only mentioned that first the attacker resolves, and then the defender.

This yields to a confusion that could mean a powerful combo for the Dwarves - combining the Digging Machine and War Machine.

Both have got "Resolution" abilities - one which leads to discarding cards from hand, and the other which destroys cards from the discard pile.

Does this allow for a combo, in which a 3-gold card is discarded to add 3 Strength to the Digging Machine, and then automatically destroyed in order to give yield another 4 Strength for the War Machine's ability.

First thing's first, the War Machine will add only 1 strength to the Digging Machine as the ability reads "give 1 strength to EACH OTHER unit". It omits the War machine itself so if you have no other units in this battle, it will yield only 1 additional strength.

However, the Digging machine can discard two gold cards, so a single Digging machine can give up to 6 additional strength. The combo you describe is ok, it gives a total of 13 strength from two units that cost a total of 11 and you destroy an additional 3-gold card. In other words, you are gaining 13 strength for 14 gold investment, so I wouldn't say it is broken or that powerful. Humans for example can go pretty easy over 12 early in the game for a 1:1 strength:gold ratio, and they will do it consistently unlike the combination you describe, which would require at least a turn to reset, not to mention the destruction of a valuable 3-Gold card.

TL;DR - the combo you describe is valid per the rulebook, the total strength gain is lower than you wrote, and it is definitely not that overpowered compared to things other factions can pull off.