For Turkey to join the war they would demand massive military aid to assist in the defense of their eastern border against British (and possibly) Soviet attacks. Turkey would be a rather valuable ally to Germany as Turkey was where they got shipments of Chromite Ore, a vital component in Stainless Steel production so they would likely be willing to send military aid just to make sure that those shipments don't stop. Speer had a comment to the attune of "Without those shipments, production would halt within six months". I can't find the exact quote right now. Will provide a link when I have more time to dig through some sources.
Turkey had a peace time army of 174,000 men which didn't start seeing increase until the start of 1940, at that time they mustered ~230,000 men, one armoured brigade, and three cavalry brigades with four corps stationed in the eastern "frontiers" of the nation, one corps in Thrace and one in reserve. But almost all of the equipment was pre-WW1 with rifles like the Lee Enfield, Lebel, Masuiers etc. being used, this could easily be remedied with Italian or German made weaponry but it is still something to consider. They had fortifications along the Dardanelles and along the outer regions of the country to the East, including heavy works at Erzurum, Kars, Adana amoung some others. The airforce was 370 planes of all type with only about half of them being modern even though they had over 8,000 men in their airforce.
Depending on when Barbarossa takes place, this could potentially spell an interesting picture for the med. theater. The Turkish and Romanian navy could both possibly come to bare against the British, especially if a campaign in Greece and North Africa takes place. So long as the Soviets don't get involved, that would add two (albiet weak) navies to aid the Italians in action. The Turkish navy consisted of the outdated battle cruiser Yavuz (ex-Goeben), 4 destroyers, 5-6 submarines, 2 light cruisers, 3 mine-sweepers, 2 gunboats, 3 motor torpedo boats, 4 minelayers and a surveying vessel. The Romanian navy consisted of four destroyers, twelve torpedo boats, four gunboats, six minelayers, three amphibious landing self-propelled barges, four submarine chasers, three submarines and five midget submarines.
It could also allow the Black sea to be under "axis control", with Italian and German ships (as well as the Turkish and Romanian navy) to defeat Filipp Oktyabrsky and prevent the vital aid the fleet gave to important sieges like Odessa in 1941 (evacuating 86,000 soldiers and over 150,000 civilians), Sevastopol that could make the city fall at the end of 1941 instead of mid 1942. This would also prevent the counter-attack at Kerch and (possibly) allow the Germans to cross over the straight themselves or be able to have the 11th army properly act as the flanking guard for AGS at the start of 1942 like they were instructed too and allow an additional 600 aircraft (including a heavy mix of Medium bombers, and dive bombers) to be deployed elsewhere. Wiking or ObssesedNuker would know much more regarding that then me though.
For Yugoslavia it wouldn't make much a difference all-told. The nation had about 4,000 artillery pieces, many were aged and horse-drawn, around 1,700 of these were relatively modern, including 812 Czech 37mm and 47mm anti-tank guns. There were also about 2,300 mortars, including 1,600 modern 81 millimetres pieces, as well as twenty-four 220 millimetres and 305 millimetres pieces each. Of 940 anti-aircraft guns, 360 were 15 millimetres and 20 millimetres Czech and Italian models. All of these arms were imported from different sources, which meant that the various models often lacked proper repair and maintenance facilities. The only mechanized units were 6 motorized infantry battalions in the three cavalry divisions, six motorized artillery regiments, two tank battalions equipped with 110 tanks, one of which had Renault FT models of World War I origin and the other 54 modern French Renault R35 tanks (which out-performed Panzer III's to a large extent) plus an independent tank company with eight Czech SI-D tank destroyers.
Fully mobilized, the Yugoslav Army could have put 28 infantry divisions, three cavalry divisions, and 35 independent regiments in the field. Of the independent regiments, 16 were in frontier fortifications and 19 were organized as combined detachments, around the size of a reinforced brigade. Each detachment had one to three infantry regiments and one to three artillery battalions, with three organised as "alpine" units."