They themselves believed they had valid reasons, which I will explain further, but shortly, they invaded Norway to stop a possible Allied invasion of Norway, and Denmark stood in the way. And Yugoslavia signed a non-aggression pact with the Axis only to have that government ousted in a coup and the pact torn apart, that gave Germany a casus belli, at least in their eyes.

Denmark was in the way to Norway, and since many in the German High Command (including Hitler) believed that the Allies planned to invade Norway and cut into Sweden to strangle Swedish iron exports to Germany (Churchill did plan something like that, Plan R 4, and earlier France and Great Britain planned to invade Norway and push through Sweden to reach Finland during the Winter War). So if one considers that a valid excuse to invade Denmark and Norway then you have your casus belli. Germany didn't launch Operation Weserübung just because they could, they had (in their eyes) a valid strategic reason for it.

As for Yugoslavia. In 1940, Fascist Italy grew more and more aggressive. Mussolini’s Foreign Minister, count Galeazzo Ciano attempted to make Vlatko Maček (leader of the Croatian Peasant Party) to cut ties with Serbia and under Italian “protection”, an independent Croatia (except Dalmatia, who the benevolent Italians would administer) would be created. Maček declined, and under orders from Hitler, a furious Mussolini was forced to scrap his plans to invade both Yugoslavia and Greece in March 1940.

Yugoslavian leaders were very much aware of what a race against time they had before them, and likewise knew it would take extremely delicate and skillful diplomacy. Prince Paul tried to avoid formally binding Yugoslavia to Nazi Germany. The constant threat of an Italian invasion made him seek closer ties with France and Great Britain. When the French army collapsed in May, a shocked government in Belgrade even began initiating diplomatic talks with the Soviet Union, which the anti-communistic Yugoslavia had thus far refused. On 28 October 1940 Mussolini decided to ignore his German ally; Italy attacked Greece. 

Meanwhile, the performance of Italian troops in North Africa was abysmal, a military disaster, and Germany had already sent troops there to prop up their Fascist ally. Once they had arrived, German commanders said they wanted provisions and war material to reach them via the shortest route, i.e. through the Balkans. Newly appointed Prime Minister of Great Britain, Winston Churchill, countered this by sending several divisions to Greece.

Unfortunately, this placed Yugoslavia in a hopeless situation, caught between a rock and a hard place. Belgrade HAD to pick a side now, German pressure was immense. Bulgaria had already declared war on Great Britain, and allowed German supply depots to be sent through Bulgaria, along with German troops.

The Yugoslavian government and Prince Paul tried for as long as they could to not have to join the Axis Powers, who now consisted of Germany, Italy, Japan, Hungary, and Bulgaria. 

That the bell would toll for Yugoslavia soon was clear to everyone. When 350 000 German troops arrived in Bulgaria in March 1941, Yugoslavia felt they had no other option than to negotiate with Germany. Prince Paul initially refused to openly sign a pact with Germany. The Yugoslavian ambassador to Germany (the future Nobel literature prize winner), Ivo Andrić, was told to stall for time as long as he could. But German pressure was too much, and on March 25, Yugoslavia officially signed a pact with Germany and Italy.

The pact was signed even though Prince Paul and the government knew that most Serbs immensely despised Germany, remembering all too well the First World War. The signing of the pact was a political death sentence for Prince Paul and the government.

A mere two days later, on 27 March, a bloodless coup ousted the Prince Regent and the Cvetković government. The protesters made young Peter their King (as Paul had been Prince Regent until Peter would come of age). And this coup is what finally lead to the destruction of the first Yugoslavia.