Can I use spells without the keyword Action and Reaction during my opponent's turn?

No. Spells without Action or Reaction can only be played during your own turn, in an open state with nothing on the chain — never on your opponent's turn.

To play a spell while it's not your turn, it must have Reaction (lets it be played in a closed state on any player's turn, e.g., responding to a chain) or Action (lets it be played during a Showdown on any player's turn). A spell with no timing keyword has neither permission (Rule 155; Rule 806.1.b; Rule 813.1.c.1).