「がんぐ」 and 「おもちゃ」 both mean “toy” but they have different origins.
The origin of 「おもちゃ」 can be traced back to Heian period. It had a different form and sound at the beginning but the meaning was 「てに もって あそぶもの」 ”something you can play with by using your hands”. 「おもちゃ」 itself doesn’t have Kanji.
Kanji 「玩」 has Chinese sound “on-yomi”; ガン and Japanese sound “kun-yomi”; もてあそぶ. The meanings are “to play with”; “to appreciate”, so it started to be used to indicate 「おもちゃ」. 「具」(グ)means “tool” and the word 「玩具」 to mean “toy” is relatively new compared to おもちゃ. (From Meiji period)
When 「玩具」 first appeared, it was supposed to be read as がんぐ according to the original sounds the kanji had. However, since both「玩具(がんぐ)」 and 「おもちゃ」 could indicate the same thing (toy), we started to use 「玩具」 as kanji for 「おもちゃ」.
So you can use both 「ガング」 and 「オモチャ」 (katakana indicates just “sounds”) for 「玩具」 and the meaning is the same but formality may differ. In general, we use 「オモチャ」 in speech. Children wouldn’t understand 「ガング」. Even in writing we usually use hiragana 「おもちゃ」. In formal writing, 「玩具」 is used but how you read it (ガング or オモチャ)depends on the context. Some names of organizations or companies should be read as 「ガング」 (for example 「日本玩具協会(にほんがんぐきょうかい)」 and we have fixed expressions like 「知育玩具(ちいくがんぐ):educational toys 」. And 「玩具業界(がんぐぎょうかい)」 ”Toy industry” can be divided into two categories ; おもちゃ業界 and ゲーム業界(in this usage 「おもちゃ」 and 「ゲーム」 are sub-categories in 「玩具(がんぐ)」.
As for 「玩具会社」, it can be read as 「おもちゃがいしゃ」
For your personal use, I would suggest that you should avoid using kanji 「玩具」. 「オモチャ」 as sounds and 「おもちゃ」 in writing are far more common in our everyday life.