Let's think about what each of these categories represent?
Death Ray or Poison
For me, the key to Death Ray or Poison is the poison. How well does your body resist the effects of poison and dying? To me that means this is basically a Constitution save, also useful for saving against disease and perhaps surviving 0 hit points. In a game with a single saving throw, I'd allow modifying the roll by a Constitution modifier.
Why are magic wands treated differently than staves and spells? I don't have a good answer for this. So I took a page from _Harry Potter_ and _Lord of the Rings_. In Harry Potter, everyone has a wand and most of your magic is performed using it. People leap out of the way when someone starts pointing a wand. In LotR, Gandalf has a staff. I can't recall any instance when he pointed his staff to cast a spell. He stomped the staff to break the bridge in Khazad Dum. He lit the end of it for light. I imagine effects from the staff cannot be dodged, but perhaps resisted. So, for me, the Magic Wand save is a physical avoidance of the danger, and the Staves and Spells save is resistance to magic.
So, I'd use the Magic Wand save for any effect where you must use your dexterity and agility to avoid something. Jump out of the way of the pit trap or the laser beam, dodge the mechanical blow darts, or grabbing the rope that dangles over the cliff. Basically a DEX save. In a game with a single saving throw, I'd allow modifying the roll by a Dexterity modifier.
Paralysis or Petrification
Seriously, I'm completely stumped on how to generalize this saving throw. Perhaps to anything where one's movement is restricted, like being tied up. But what modifier to apply to a single saving throw? No clue.
Dragon Breath is not aimed at one person, it covers an area. So, the Dragon's Breath save could be used for any area-effect danger. That chest really was trapped, and now you need to jump out of the way of the poison gas. In a game with a single saving throw, I'd allow modifying the roll by a Dexterity modifier. I'd also make the save +2 to +4 harder than the standard save, since avoiding an area effect is harder than avoiding an aimed effect, like the Wand.
Rods, Staves, or Spells
This is your basic magic resistance save. Add the Intelligence modifier to a single saving throw as willpower, which is how some games do this. If the effect is aimed and requires a to-hit roll, use the Wands saving throw instead.
So, I'm not sure what this means for my nascent game. But thinking about these is helping me decide.