Taking Over Europe
It seems to me that the aims of the opponents are as follows:
Aggressive play seems likely given the cards held and trenches dug. I would try to avoid the fight this round and then move on my next go.
The optimal outcome would be for a corrosive war to kick off over South America. It is beneficial since it is far away from me. This would be my aim.
Thus whilst Red can solidify its situation by taking the armies now, I believe appearing weak whilst trying to halt Green's ambition in Europe is the main goal in this round. There are many rounds left in the game and even without taking the armies now Red is in no danger of losing Australia.
Therefore I will not cash my cards. I would announce the moral high-ground verbally committing to stop green from taking over Europe. Then I place my armies in Afghanistan and attempt to take all of Green's single army territories in Europe. Once finished, I would then move my left-over armies south away from Greenland. The aim is to offset my aggressive move whilst showing no future plans for expansion. I am therefore hinting that my European territories are available for cards, and I do not intend to take over the whole continents in a rush. This reduces the backlash pressure when everyone may try to stop me getting the bonus of Europe in the next turn.
This should show a willing to fight but with a passive nature. By refusing to cash the cards, and ending up with 4 cards in the next round, I should also look dangerous.
Hopefully, I would appear dangerous to confront but no threat, hence best avoided.
Blue will play a consolidation strategy for North America, taking Greenland and building up forces to the south, as Asia is currently unconquerable.
Green will want to avoid a corrosive war over Europe, which it is unlikely to win as I will have the northern territories whilst blue will have Greenland and neither yellow or I would let it happen. Hence, Green would get into a long conflict with Blue over North and South American continents and is basically in a perilous position.
Yellow will see little value in attacking me as I appear passive and I have large armies nearby which can be used defensively if I want to. Yellow can see that Green is continuously under pressure, and as a result may focus on getting South American continent.
If all goes according to plan, Europe should be relatively low on peoples agenda and shy on armies. Most of the focus should be on South America and a conflict should have broken out, heavily weakening the two opponents. Meanwhile I should be relatively unharmed, maybe minus a few easily conquerable territories.
With 10+ armies from my cards, I have a chance to make a reasonable play at taking and holding one of Europe or Asia next. If I took Asia I would try to hold, whilst if I got Europe I would still try to leave it for Asia. If I got Australia and Europe, this leaves no one else any territories to fight over except those that are Red!. Not nice. Taking Asia instead, leaves them something worth chasing after (the carrot) whilst I can still limit access routes and play a significant political role in the game.