Hi Robert,

The above Triggers looks good may be you have any other workflow field update or Process builder or some other trigger which updates the Opportunity.

To avoid the recusive you have to Static boolean variable to make the trigger fire only once.

-----------
Create this below Apex class:

public class RecursiveTriggerHandler{
     public static Boolean isFirstTime = true;
} 

-------------

Call the above class in your apex trigger  if conditons like below:

trigger UpdateOTRev on Opportunity (after insert, after update) {
    Set<id> triggerIds = new Set<id>();
    List<OpportunityLineItem> lstOLIUpdate = new List<OpportunityLineItem>();
     if(RecursiveTriggerHandler.isFirstTime)
     {
        RecursiveTriggerHandler.isFirstTime = false;
    for(Opportunity Opps : Trigger.new){
        triggerIds.add(Opps.Id);
    }
    List<Opportunity> lstOpps = [SELECT id, CloseDate, (SELECT id, TotalPrice FROM OpportunityLineItems) FROM Opportunity 
                                 WHERE id in: triggerIds];
    for(Opportunity opp: lstOpps){
        for(OpportunityLineItem oli : opp.OpportunityLineItems){
            
            if(opp.CloseDate > Date.valueOf('2017-12-31') && opp.CloseDate < Date.valueOf('2018-04-01')){
                oli.Test_Q1_2018__c = oli.TotalPrice;
                oli.Test_Q2_2018__c = 0;
                oli.Test_Q3_2018__c = 0;
                oli.Test_Q4_2018__c = 0;
                oli.Test_Q1_2019__c = 0;
                oli.Test_Q2_2019__c = 0;
                oli.Test_Q3_2019__c = 0;
                oli.Test_Q4_2019__c = 0;
                lstOLIUpdate.add(oli);              
            }//END if 2018 Q1
            if(opp.CloseDate > Date.valueOf('2018-03-31') && opp.CloseDate < Date.valueOf('2018-07-01')){
                oli.Test_Q1_2018__c = 0;
                oli.Test_Q2_2018__c = oli.TotalPrice;
                oli.Test_Q3_2018__c = 0;
                oli.Test_Q4_2018__c = 0;
                oli.Test_Q1_2019__c = 0;
                oli.Test_Q2_2019__c = 0;
                oli.Test_Q3_2019__c = 0;
                oli.Test_Q4_2019__c = 0;
                lstOLIUpdate.add(oli);              
            }//END if 2018 Q2
            if(opp.CloseDate > Date.valueOf('2018-06-30') && opp.CloseDate < Date.valueOf('2018-10-01')){
                oli.Test_Q1_2018__c = 0;
                oli.Test_Q2_2018__c = 0;
                oli.Test_Q3_2018__c = oli.TotalPrice;
                oli.Test_Q4_2018__c = 0;
                oli.Test_Q1_2019__c = 0;
                oli.Test_Q2_2019__c = 0;
                oli.Test_Q3_2019__c = 0;
                oli.Test_Q4_2019__c = 0;
                lstOLIUpdate.add(oli);              
            }//END if 2018 Q3
            if(opp.CloseDate > Date.valueOf('2018-09-30') && opp.CloseDate < Date.valueOf('2019-01-01')){
                oli.Test_Q1_2018__c = 0;
                oli.Test_Q2_2018__c = 0;
                oli.Test_Q3_2018__c = oli.TotalPrice;
                oli.Test_Q4_2018__c = 0;
                oli.Test_Q1_2019__c = 0;
                oli.Test_Q2_2019__c = 0;
                oli.Test_Q3_2019__c = 0;
                oli.Test_Q4_2019__c = 0;
                lstOLIUpdate.add(oli);              
            }//END if 2018 Q4
        }//END For(OpportunityLineItem)
    }//END for(Opportunity)
    if(lstOLIUpdate.size()){
        update lstOLIUpdate;
    }
}
}


Reference Links:

http://www.sfdcpoint.com/salesforce/avoid-recursive-trigger-salesforce/
https://help.salesforce.com/articleView?id=000133752&language=en_US&type=1
http://www.infallibletechie.com/2012/08/recursive-triggers-in-salesforce.html
http://sfdcbeginner.com/stop-recursive-trigger-in-salesforce.html


Can you please Let me know if it helps or not!!!

If it helps don't forget to mark this as a best answer!!!

Thanks,
​Raj