[SalesForce] Trigger to create task/email when Opportunity is updated with a certain stage

Hope the below code helps!

trigger TaskSubject on Task (after update, after insert) {

set<id> accountIdSet = new set<id>();
//capture all the subject names in a set
//set<string> subjectName = new set<string>{'Call EJF','Email Centurion','Initiate Merion'};
map<id, list<opportunity>> opptyMap = new map<id, list<opportunity>>();
list<opportunity> updateOppList = new list<opportunity>();

//get those tasks where the tasks are related to account. Capture the account IDs in a set.
for(task t: trigger.new){
            string tempId = string.valueOf(t.WhatId);
    if(tempId.startsWith('001')){
        accountIdSet.add(t.whatId);
    }
}

//If we have any account IDs then get the associated opportuity and store the one account to many opportunity in a map<id, list<opportunity>>
if(accountIdSet.size()>0){
    for(opportunity opp:[select Name, stageName, accountid from opportunity where accountid IN :accountIdSet]){
        if(opptyMap.containsKey(opp.accountId)){
            list<opportunity> oppList = opptyMap.get(opp.accountId);
            oppList.add(opp);
            opptyMap.put(opp.accountId, oppList);
        }else{
            list<opportunity> newOppList = new list<opportunity>();
            newOppList.add(opp);
            opptyMap.put(opp.accountId, newOppList);
        }
    }
}

//If we get the opportunities then change the stage.
if(Trigger.isUpdate && opptyMap.size()>0){
    for(task t: trigger.new){

 //Check if the subject of the task is one among the set 
 //and also confirm that the subject has been changed.

        if(t.subject != trigger.oldMap.get(t.id).subject && opptyMap.containsKey(t.whatId)){

  //iterate thru the list of the opportunity associated with that account 
  //and check which of the opportunity contains the task subject in the 
   //opportunity name and update the stage to qualification

            for(opportunity oppty: opptyMap.get(t.whatId)){
                if(oppty.name.contains(t.subject)){
                    oppty.stageName='Qualification';
                    updateOppList.add(oppty);
                }
            }
        }
    }
}
if(Trigger.isInsert && opptyMap.size()>0){
     for(task t: trigger.new){
            if(opptyMap.containsKey(t.whatId)){
                for(opportunity oppty: opptyMap.get(t.whatId)){
                   if(oppty.name.contains(t.subject)){
                      oppty.stageName='Qualification';
                      updateOppList.add(oppty);
                   }
               }
            }
        }
    }
//update the oppties
if(updateOppList.size()>0){
    update updateOppList;
}
}

EDIT:
This code is working. I followed the below flow: Create an account(test account) --> Create a task for this account (test account) and make sure the subject is not 'Initiate Merion'.
create an opportunity (make sure the stage is not qualification) for the same account, name it 'test oppty Initiate Merion'.
Now edit the task created, change the subject to 'Initiate Merion'. You can now see that the Opportunity stage has been changed to 'Qualification'.

EDIT 2
Added an after insert event. Also the one more code block to handle the insert and update events seperately

EDIT 3 Task subject need not necessarily be from a set of predefined strings. As long as task subject is part of Opp name, stage must be updated

You can absolutely use an before trigger for that and it will work. That said, I typically leave the before trigger to the simpler functionality. IMO, updates to and validations against the records being acted on should happen in the before trigger, most everything else like cross object logic and callouts/emails/etc. should happen after. But there is nothing that says you can't create records before if you desire.