Sorry for the long post!
The reason most people fail to see why Sp-Sw-Tu joining would be a major boost is that they are used to the 1944 ww2 situation, not the 1940-1942 ww2 situation.
IF the war stretches to 1943-44 then yes, the US production numbers are going to have a serious effect on the war, and potentially eventually turn it into an axis defeat.
But until the increased US production starts having a serious effect on the European theather, thats not the real question is it.
The real question is how long do you give the Axis powers to fortify Europe before the US enters the war, and just how determined the US is to slug it out.
We know in hindsight that as long as the going was good, the US would stay in the war. So, lets then safely say that the US is unlikely to accept a peace unless left entirely alone, and at which point it would be NK-SK style "peace"
The real effect of Spain joining is the shortening of the Axis defensive perimeter from the entire Med coastline to just the E-med coastline. Since no Allied amfb convoy would try to run the two blockades(gib/sicily). Gib falling is irrelevant as long as the function of Gib can be filled without Gib itself. In other words. IF you use airpower to firstly force the fleet away from Gib (or turn it into one giant one-sided sinking match if the UK tries to hold onto the naval presence in Gib for months) you can effectively blockade both Gib and the entire W-med
The presence of Gib would of course inhibit axis shipping through the straits as well, but that is of far lesser importance since its possible to unload cargo anywhere in Spain-France and move it overland to any Spanish-French Med city and reload there. It would be a logistics hassle but still, hardly a major setback.
It would be entirely possible for the Axis to ignore the Spanish railroad infra and use the port system. It might not be pretty but it can be done.
So, Spain joining secures the entire W-Med from any allied invasion until either Sicily or Africa falls to the Allies.
The only really threathened Spanish area would be the Canaries. And if you have ever been to those islands, you'll agree when I Say, good luck in trying to mount a succesful amfb operation against a Axis military that is determined to hold onto the islands. In 1943-44 it might be possibly but absolutely not in 1941 or 42. The UK simply doesn't have the naval power required to both project aerial superiority and secure the landing zones against the massive German response that would follow any attempt. And you don't start island hopping if you got a land border with the Axis, which the UK would have.
The next question is if Spain closes the W-Med and Turkey joins is it enough to force the UK out of the Suez. The UK Would make it the fight of its life but it might not be enough. It would go on for months but if it doesn't work for the UK, then its game over.
Because the occupation of the Suez would allow every single axis unit in the med to be moved to E-Front, no need to garrison anything in the med anymore. Combined with the now entirely secure South-European industry that the UK just can not hit. There goes the Ploesti oil raids and the constant threat of air attacks against Italy, Bulgaria, Romania and so on.
While Turkey and Spain are both militarily relatively small, the impact they can have IF they both focus on 1 thing at a time is massive.
Spain will be able to render W-Med inaccesible to the allies, and it will be able to hold onto the Canary islands well into the 1943 giving the UK a serious headache. Especially if Germany stationes 200 or so dive bombers for anti-convoy duty with secondary emphasis on attacking any invasion fleets.
So, Spain provides a incredibly good Anti-Convoy base in the Atlantic, and frees the entire W-Med from axis having to garrison any of it. In exchange for requiring food imports and possibly some help with its atlantic wall. IF it can actually spare units its a slight bonus, the main effect being the Gib-Med-Canary
Same applies to Turkey, militarily mostly irrelevant its position allows it to play a key strategic role. The UK position in the Mid-East at about the first battle of El-Alamein was precarious. The addition of even one fully armored German corps in Iraq supported by luftwaffe from its Turkish airbases and with what ever secondary turkish land units that can be spared would be a serious problem. Add to that the already brewing anti-UK sentiment in the middle east and the possibility of German armies swooping in, the situation might be entirely un-managable for the UK.
It's impossible to say with certainty but judging by the military situation after Rommel was sent to Africa, the addition of losing the Gib and Axis forces advancing south through the mid-east the UK might actually lose its middle-east holdings.
Once again, this is mostly relevant because it allows the axis units to redeploy from the E-Med to either Eqypt-Sudan border or the E-Front. Even if they later lose the Suez again, it is possible to destroy the channel so entirely that it will take months if not years to open again.
While both Turkey and Spain are militarily relatively small on their own, the opportunities to the axis that they provide, are massive indeed.
Swedens major commitment would be in resource production for its axis partners, such as food. But it could mobilize about 400.000-1.200.000 million men of various quality between 1940 to 1945 while being at peace. Certainly not a massive amount but well motivated and lead, could flip the favor in a few major engagements, not enough on their own but still, quite good.
It all depends on the POD that is used to allow the three to join.
The following might be accetable:
Winter war escalates and Sweden joins the war, later the two join the axis in later 1940 or early 1941. Followed by both having a massive re-armament similar to what Finland had in 1940.
Franco dies during the SCW and the new guy in charge is pro-axis instead of pro-neutrality and eyes the war looking for a good opportunity to join. Spends 1-2 years after SCW to fortify its atlantic coast, prepare to invade gib and fortify Canary and expand the airbase and ports there.
Turkey is a bit more difficult so I cant really say.
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TL

R:
Spain secures W-Med and allows axis units there to transfer to the E-Front.
Spain offers Canary islands to the Axis for U-Boat and Dive Bomber use.
Spain shortens the Axis defensive perimeter from the W-Med to simply the Spanish atlantic Coast.
Turkey offers the Axis a real shot of taking the Suez.
Sweden offers the Axis a increased food + resource production and enough extra force to take both Leningrad and Murmansk when combined with the inherent increase in the Finnish desire to fight.
The three combined would allow such a additional deployment of force against the SU in 1942 that even the vaunted Red army would be on the ropes.
In 1942 you might be looking at a situation where the UK has not won a major engagement in the war other than BoB and has lost every major land engagement with the Axis from the start of the war.
Where the SU has lost Leningrad, Murmansk, Stalingrad and by the 1943 spring is facing a three directional push towards Moscow.
The UK would be very hard pressed to stay in the war and by 1943 spring the USSR might not be alive in any real way outside of Moscow and Siberia.