I never thought myself odd not playing with other children. Nor did I think that they didn’t want to play with me.

=I never thought myself odd because I didn't play with other children. Nor did I think that they didn't want to play with me.

参考译文：我从来不认为因不和其他孩子一起玩耍就认为我自己是很奇怪的，我也不认为他们不想和我一起玩.

1）粗体划线部分thought myself odd not playing的结构为何是这样？否定词not为何出现在中间？句子怎么翻译？

解答如下

这里not playing with，为现在分词作原因状语。

2）I didn’t think that they didn’t want to play with me.

= Nor did I think that they didn’t want to play with me

两个句子相等，是这样吗？

nor did I ..属于否定词放在句首倒装结构，表示也不，即nor放在句首需需要使用倒装结构,而且通常使用省略结构，

Tom doesn't like English. Nor do I.

Tom can't speak English. Nor can I.

Tom didn't go there.Nor did I.