I'd say that in order to merge with one another it takes both the full round action of both mini-oozes. Then, they act on the next initiative round of the one with the highest initiative.
Let's say the initiative looks like this:
- Halfling Rogue
- Dwarf Fighter
- 1/4th Ooze B
- Gnome Wizard
- 1/4th Ooze A
- Half-Orc Barbarian
- 1/4th Ooze C
- Elf Cleric
- 1/4th Ooze D
The ooze has already been split into 4 equal size mini-oozes. The Rogue goes first, then the Fighter. Then it's Ooze B's turn. It takes a full-round action to merge with Ooze A. Then the Wizard goes. Ooze A is already in the process of joining with Ooze B so it gets no further action. Barbarian goes next. Ooze C merges with Ooze D. Ooze D does not get to do anything this turn either b/c it's merging with Ooze C.
The next round of initiative looks like this:
- Halfling Rogue
- Dwarf Fighter
- One-Half Ooze B
- Gnome Wizard
- Half-Orc Barbarian
- One-Half Ooze B
- Elf Cleric
Again, the Rogue and Fighter go first. Then Ooze A begins to merge with Ooze B. Then all the rest go because Ooze B is already merging with Ooze B.
On the third round all the mini Oozes have merged together to reform their original Ooze (with fewer HP, though).
The final initiative order looks like:
- Halfling Rogue
- Dwarf Fighter
- Full-size Ooze
- Gnome Wizard
- Half-Orc Barbarian
- Elf Cleric
If the party reduces the Ooze to 1/2 HP again, it splits into 1/2 Oozes A and B again. If one of them gets reduced to 1/2, they split as well. And the process continues until there's no more Ooze to reform with itself.