First Oliver and then Omega killed Axel with Vajra and White Fang Strike respectively. The former was a 50 meter long lightning bolt comprised of hundreds of lightning bolts while the latter was a gravity law attack skill that was only second to Kahn's Dimensional Cut.
After the Hero of Fire died for the 3rd time, Ronin collected and absorbed the escaped soul again using Soul Collector. At this moment, Ronin's body was going under tremendous changes but the spirit assassin willingly halted his progress.
Stealing the souls of the saints Axel was using as Extra lives was a precautionary move made by Kahn. Because Soul Eater definitely had some more uses and Kahn didn't want to take risks and allow Axel to get any more advantages.
Who knew if he could use Soul Eater to control these souls and regain more lives? If he could, then it would be a big problem for them.