[SalesForce] Test class for After insert/update Trigger

Here's a commented rewrite of that trigger which does not execute the aggregateResult query within the loop context of the Trigger.new collection.

Additionally, there's some code in both of your triggers which don't actually do anything as written.

trigger fulfillmentcontactcreatedopp on Opportunity (before insert, before update) {

    Map<Id, Opportunity> oppsToCheckMap = new Map<Id, Opportunity>();

    // collect the ID values of the opportunities with a stage calc value of 5 or more
    // if it is an update, the stage name must have changed
    for (Opportunity opp : trigger.new) {

        if (opp.Stage_Calc__c >= 5 ) { 

            if (trigger.isInsert || 
                trigger.isUpdate && trigger.oldMap.get(opp.Id).StageName != opp.StageName) {
                    oppsToCheckMap.put(opp.Id, opp);
            }
        }
    }

    // get an aggregate count of contact roles per opportunity in the fulfillment role
    List<AggregateResult> result = [SELECT OpportunityId
                                        , count(Id)
                                    FROM OpportunityContactRole
                                    WHERE (Role = 'Fulfillment')
                                        AND OpportunityId IN :oppsToCheckMap.keySet()
                                    GROUP BY OpportunityId];

    // iterate the results and set the number of fulfillment contacts on the opportunity
    for (AggregateResult aggCount : result) {

        /* this block of code isn't actually doing anything */
        if (aggCount.get('expr0') == 0) {

            Id oppId = (Id)aggCount.get('OpportunityId');
            Opportunity oppo = oppsToCheckMap.get(oppId);

        }
        /* this block of code isn't actually doing anything */

        // get the opportunity from the incoming map and update the value of the fulfillment contacts field
        Id oppId = (Id)aggCount.get('OpportunityId');
        Opportunity opp = Trigger.newMap.get(oppId);

        if (opp != null) {
            Integer fulcount = Integer.valueOf(aggCount.get('expr0'));
            opp.Number_of_Fulfillment_Contacts__c = fulcount;
        }
    }
}

Update

Here is the updated trigger code for the NetSuite_Sales_Order__c object with the Opportunity update statements removed from the loops. I also reformatted it for my own sanity and changed some of the odd checks for Trigger.new and Trigger.old in the if statements.

trigger celigoUpdateSalesOrder on NetSuite_Sales_Order__c (before insert, before update, before delete) {

    List<Opportunity> opportunitiesToUpdate = new List<Opportunity>();

    if (Trigger.isInsert || Trigger.isUpdate) {
        List<Id> opIds = new List<Id>();
        for (NetSuite_Sales_Order__c order : Trigger.new) {
            if (order.Opportunity__c == null) {
                continue;
            }
            opIds.add(order.Opportunity__c);
        }

        List<Opportunity> ops = [SELECT Id
                                        , StageName
                                        , StageNameState__c
                                    FROM Opportunity
                                    WHERE Id IN :opIds];

        celigo_connector__c cs = celigo_connector__c.getInstance('Opportunity Closed Stage');
        String closedStage = (cs!=null) ? cs.value__c : 'Closed Won';

        for (Opportunity o : ops) {
            if (Trigger.isInsert) {
                if (o.StageNameState__c == null) {
                    o.StageNameState__c = o.StageName;
                    o.StageName = closedStage;
                }
            }
            o.Celigo_Sync_Helper__c = true;

            // add to the list for update later
            opportunitiesToUpdate.add(o);

        }
    }

    if (Trigger.isDelete) {
        List<Id> opIds = new List<Id>();
        for (NetSuite_Sales_Order__c order : Trigger.old) {
            if (order.Opportunity__c == null) {
                continue;
            }
            opIds.add(order.Opportunity__c);
        }

        List<Opportunity> ops = [SELECT Id
                                        , StageName
                                        , StageNameState__c
                                    FROM Opportunity
                                    WHERE Id IN :opIds];

        List<NetSuite_Sales_Order__c> tOrders = [SELECT Id
                                                        , Opportunity__c
                                                    FROM NetSuite_Sales_Order__c
                                                    WHERE Opportunity__c IN :opIds];

        Map<Id, List<NetSuite_Sales_Order__c>> m = new Map<Id, List<NetSuite_Sales_Order__c>>();

        for (NetSuite_Sales_Order__c order : tOrders) {
            if (m.get(order.Opportunity__c) == null) {
                m.put(order.Opportunity__c, new NetSuite_Sales_Order__c[]{ order });
            }
            else {
                /* this code block doesn't do anything */
                List<NetSuite_Sales_Order__c> temp = m.get(order.Opportunity__c);
                temp.add(order);
                /* this code block doesn't do anything */
            }   
        }

        Set<Id> keys = m.keySet();

        for (Id i : keys) {
            List<NetSuite_Sales_Order__c> temp = m.get(i);
            Opportunity op;
            for (Opportunity tempOp : ops) {
                if (tempOp.Id == i) {
                    op = tempOp;
                    break;
                }
            }
            if (temp.size() > 1) {
                continue;
            }

            if (op.StageNameState__c == null) {
                continue;
            }

            op.StageName = op.StageNameState__c;
            op.StageNameState__c = null;

            // add to the list for update later
            opportunitiesToUpdate.add(op);
        }
    }

    // if we've got opportunities to update, do it
    if (!opportunitiesToUpdate.isEmpty()) {
        update opportunitiesToUpdate;
    }
}

The trigger code is having lot of redundancy, So I modified it. before posting the modified code few lines of explanation what I changed. you collected account Ids twice and did the condition check twice where once is more enough. I am also made changes to the test class, where Task data is provided which is not required because the trigger has to create it once the necessary conditions are met. I am expecting this trigger should work for you, if there is any errors feel free to post as a comment.

trigger OpportunityAfter on Opportunity (after update){

    Set AccountIDs = new Set();

    for(Opportunity o : trigger.new){
        if(opp.StageName == 'Closed - Lost' && opp.Business_Line__c == 'Workforce' && 
            opp.Survey_Type__c != 'APulse' && trigger.oldMap.get(opp.Id).StageName != opp.StageName){

                AccountIDs.add(o.AccountId);
         }
    }

    Task[] tasksToInsert = new Task[]{};

    for (Account acc : [Select Id, Name, OwnerId from Account where Id IN :AccountIds]){
        for (Opportunity opp : trigger.new){
            if(opp.AccountId == acc.Id){
                Task tas = new Task();
                tas.WhatId=acc.Id;
                tas.OwnerId=opp.OwnerId;
                tas.Subject='Follow-up: ' + opp.name + ' - ' + acc.name;
                tas.ActivityDate=(opp.CloseDate + 180);
                tas.Description='Follow up to see how engagement initiatives are going and if Avatar can help. Refer to lost opportunity: ' + opp.name;
                tasksToInsert.add(tas);                                                         
            }
        }
    }
    if(tasksToInsert != null && !tasksToInsert.isEmpty())
    Database.insert(tasksToInsert);

}

@isTest
public class TestClass {

    static testMethod void myUnitTest() {

    //Set up user
    User u1 = [SELECT Id FROM User WHERE Email='abc@sampleemail.com'];
    test.startTest();  
    //Run As U1
    System.RunAs(u1){

    System.debug('Testing trigger... (single record validation)');

    //NEW Account record
    Account acc = new account();
    acc.Name = 'Test Account';
    acc.Industry = 'Healthcare';

    insert acc;

    //NEW Opportunity record
    Opportunity opp = new Opportunity();
    opp.Name = 'Test Opportunity'; 
    opp.CloseDate = System.today();
    opp.StageName = 'S1 - Investigative';
    opp.Type = 'Repeat Business - Wrkforce HC';
    opp.AccountId = acc.Id;
    opp.Survey_Type__c = 'Product Name';

    insert opp;

    opp.StageName = 'Closed - Lost';
    opp.Reason_Won_Lost__c = 'Relationship';
    opp.Business_Line__c = 'Workforce'  //added this line to meet the if condition while collecting the set of id in the trigger.

    update opp;
   test.stopTest();
    // Here I am expecting the task has been inserted and doing a query for it         and check it in the assert statement.
   Task  testTask=[Select Id, WhatId from Task where WhatId=:acc.Id];
    //Validate single insert
    System.assertEquals(acc.Id, testTask.WhatId);

    }
    }
}