Pausing a battle, concluding others, then coming back to it?

No, once you start a battle you have to finish it, or retreat before you can go to the next battle (pausing to conduct a different battle, then returning later isn’t allowed). Read the General Combat rules on pg #18 of the Europe 1940 2nd edition (I’m sure the rule it is the same in the 1st edition).

The 3rd sentence says:

“Combat in each space takes place at the same time, but each affected territory or sea zone is resolved separately and completely before resolving combat in the next contested space.”

Of course, you as the attacker have the choice of which battles you want to roll first and what order you want to resolve all the battles. So while it may not help you in a mid-battle situation, you can decide if you have one battle that maybe kind of hinges on the outcome of another battle to do the other battle first and see the results.
What I usually like to do is resolve all sea battles first, from the smallest to the largest, then all small land battles and then the larger land battles.
For example: If I am Germany, a typical first round combat move would be to go after the Royal Navy in sea zones 91, 109, 110 and 111. On land I go after Normandy, France, Southern France and Yugoslavia. Sometimes I will also send a couple of planes after the French ships in SZ 93. That last one depends on how confident I am whether or not our UK player will scramble into SZ 110 and how confident I feel about the forces attacking Paris.
In order, I resolve the sea combats first: 2 subs vs. cruiser in SZ 91 – 2 subs vs. DD and Transport in SZ 106 – 1 sub, 1 BB, 1 ftr, 1 tac and 1 bomb vs. 1 BB, 1 CA, 1 DD and maybe 1 ftr (from Scotland) in SZ 111 – then I will resolve SZ 110 which will usually be the biggest sea battle.
If I don’t think UK will scramble, then I send 2 ftr, 2 tacs and 1 bomber against 1 BB and 2 CA. That is when I might send 1 ftr and 1 tac against the French CA and DD in SZ 93.
If I do think UK will scramble, then I leave the French ships alone in SZ 93 and send 3 ftr, 3 tacs and 1 bomber against 1 BB, 2 CA and 3 ftr. Of course, if UK decides to save his fighters for later, then it is kind of a waste of planes for me totally overpowering the ships and not getting to attack somewhere else. Then again, if I don’t send those extra 2 planes and UK does scramble, I could end up getting slaughtered.
After that, I move on to the land battles. First Normandy, then S France, then the big France battle and finally Yugoslavia. I do Yugoslavia last even though it is smaller than the France battle because it has no effect at all on any of the French battles and it is a neutral.
Also, I use the FMG Combat Dice so I like to resolve battles with one nation before switching to different dice for another nation.
Well, it looks like I just talked your ear off to make a simple point: small sea battles to large sea battles, small land battles to large land battles.