Do Germany and Japan have strong armies..are they allowed to build an army after WW2?

Japan has one of the world's strongest militaries, characterized by high levels of training and excellent equipment in a not-inconsequential size. While it lacks certain capabilities of a primarily "offensive" nature and lacks extensive experience of operations overseas, it is still highly capable of defending Japan, which is its primary role. Restrictions on the Japanese military are domestic in nature - if the Japanese government decides to change them, they are well within their rights to do so, provided they do not violate any international treaties to which they are a party (none of which specifically target Japan).

Germany has a very professional, highly trained, and well-equipped military, but it is not that large, even in comparison to its neighbors (Britain, France, Italy, and Poland all have larger militaries). Germany's military is limited by treaty (the Final Settlement Treaty), but by the terms of that treaty Germany can legally have a military twice its current size. However, the Russian withdrawal from the Treaty on Conventional Armed Forces in Europe renders the situation more complicated.