Since Sid covered Romania, I'll do Hungary:
(noted for their baroque insignia, retro WWI uniform styling and utterly charming womenfolk!
BTW: The Horthy government ONLY declared war on the Soviet Union. Not the US or UK.
8th Army Corps (1st Mountain Bde, 8th Border Guard Bde)
Mobile Corps (1st cav. Bde, 1st & 2nd Motorized Bdes)
units mostly employed in rear guard activities, additional troops sent forward to bolster units until unit strength was to 2 full Corps
Hungarian 2nd Army
3rd Army Corps (6th, 7th & 9th Light Infantry Divs)
4th Army Corps (10th, 12th & 13th Light Infantry Div's)
7th Army Corps (19th, 20th, 23rd Light Infantry Divs)
1st Armored Div
2nd Air Brigade of Hungarian Airforce
2nd Army sustained heavy losses along the Don River sector of the front, especially to the 3rd Army Corps. Remainder of 2nd Army was used to hold the left flank of the 1942 offensive with the German 6th Army at Stalingrad. In January, 1943 Soviet forces broke through the overextended and thinly stretched Hungarian lines, and the 2nd AG was destroyed in all but name. 35000 KIA, 26000 POWs, to include the father of one of my college friends (he survived. Many did not)
7th Army Corps (1st, 5th, 9th, 12th & 23rd Light Infantry Divs)
8th Army Corps (18th, 19th, 21st & 201st Light Infantry Divs
aforementioned Carpathian Group
Losses sustained at Kharkov (1st LI reduced to 50% strength in 2 weeks fighting in Sept 1943), by Dec. 1943 only 2 divisions managed to escape destruction, via a retreat through the Pripet Marshes and to the Polish Border.
1st Army Group
6th Army Corps (25th, 27th, 201st Light Infantry Divs)
7th Army Corps (16th, 18th Light Infantry Divs)
2nd Armored Div
24th Light Inf Div
1st Mountain Bde
2nd Mountain Bde
20th Infantry Div
At this point German forces had entered Hungary
2nd Army Group
2nd Army Corps (2nd Armored Div, 7th & 9th Replacement Divs, 1st & 2nd Replacement Mountain Bdes)
9th Army Corps (2nd Field Replacement Div, 25th Inf Div, 27th Light Inf Div, 9th Borderguard Bde)
Units sent to Transylvanian front after Romania left the Axis
In October 1944 the Horthy government was overthrown, must mention also a couple of additional Hungarian units, under complete German command:
18th WSS Div "Horst Wessel"
22nd WSS Div "Maria Theresa"
25th WSS Div "Hungaria"
26th WSS Div "Hunyadi"
The latter two were EXTREMELY poorly equipped and supplied, as I recall the 26th was nicknamed the "slouch hat division" as much of the unit was in civilian clothing with only cap badges on their "Kossuth" type fedoras.
(One of the Ballantine books on the WSS, also the L & F Funcken volume on SS makes mention of the 26th being the WSS unit that "disappeared". Umm, they never all got uniforms, no supplies, hopeless situation at the front. "Disappearing" would have been a VERY sensible thing to do!)
(FWIW, I will also mention Croatia's contribution of the 369th "Schachbrett" Div to the fighting at Stalingrad! There. I have mentioned them!)