noteandtask_controller

public class noteandtaskcontroller
{
    public List<SObject> record1 {get; private set;}
    public final Datetime value; 
    public String actId; 
    public List<SObject> sortedRecords {get;set;}
    
    //taking in parameter 'controller' to pull account Id for query
    public noteandtaskcontroller(ApexPages.StandardController controller) 
    {
        actId = controller.getId(); 
        //creating a new list called wrappers
        List<myController> wrappers = new List<myController>();  
          //querying tasks
        record1 = [Select CreatedById, Subject, Description, CreatedDate, Date_Activity_Logged__c 
                  From Task 
                  WHERE Status = 'Completed' AND (AccountId = :actId OR WhatId = :actId OR WhoId = :actId)];
        //looping through record1 aka tasks and then creating a new list called myController and adding the task's date activity logged. And then adding this list to the wrappers list.
        for (SObject rec : record1) {
			 wrappers.add(new myController(rec, 'Date_Activity_Logged__c'));  
		}
     //querying notes
        record1 = [Select CreatedById, Title, Body, CreatedDate From Note WHERE ParentId =: actId];
        //looping through record1, now notes, and then creating a new list called myController and adding the note's CreatedDate. And then adding this list to the wrappers list.
        for (SObject rec2 : record1) {
			 wrappers.add(new myController(rec2, 'CreatedDate'));  
		}           
        //sorting
        wrappers.sort();
        sortedRecords = new List<SObject>(); 
        //looping through list 'wrapper' and adding to sortedRecords the wrapper's record----????
        for (myController wrapper : wrappers) sortedRecords.add(wrapper.record);
        system.debug('this is the list: ' + wrappers);
        
    }
    
    public class myController implements Comparable 
    {       
        private SObject record;
        public Id id;
        private Datetime value; 
        //creating new controller that takes in two params (record and field)
         myController(SObject recordobj, String field)
        { 
            //pulling the record ie task or note being passed in- and pulling out the id, CreatedDate or Date_Activity_Logged__c, and the record name
            this.record = recordobj;
            this.id = recordobj.Id;
            this.value = (Datetime)recordobj.get(field); 
        } 
        
        public Integer compareTo(Object instance) 
        { 
            //comparing the param to the next spot in the list (the list always changes so we are comparing to an instance)
            myController that = (myController)instance; 
            //if value is equal we return 0, if greated then we return 1, if less then we return -1, this automatically builds the list in order
            if (this.value == that.value) return 0;  
            return (this.value < that.value) ? 1 : -1; 
        } 
    }
}

<--------------VF PG---------------->
<apex:page standardController="Account" extensions="noteandtask_controller">
    <apex:pageBlock >
        <apex:pageBlockTable value="{!sortedRecords}" var="record">
            <apex:column headerValue="Title/Subject">
                <apex:variable var="field" value="{!IF(BEGINS(record.Id, '002'), 'Title', 'Subject')}" />
                <apex:outputField value="{!record[field]}" />
            </apex:column>
            <apex:column headerValue="Body/Comment">
                <apex:variable var="field" value="{!IF(BEGINS(record.Id, '002'), 'Body', 'Description')}" />
                <apex:outputField value="{!record[field]}" />
            </apex:column>
            <apex:column headerValue="Completed Date">
                <apex:variable var="field" value="{!IF(BEGINS(record.Id, '002'), 'CreatedDate', 'Date_Activity_Logged__c')}" />
                <apex:outputField value="{!record[field]}" />
            </apex:column>
            <!--<apex:column headerValue="Created Date">
                <apex:outputField value="{!record['CreatedDate']}" />
            </apex:column>-->
            <apex:column headerValue="Created By">
                <apex:outputField value="{!record['CreatedById']}" />
            </apex:column>
        </apex:pageBlockTable>
    </apex:pageBlock>
</apex:page>

Instead, use an inner class:

public class MyController
{
    public List<SObject> records { get; private set; }
    public MyController(...)
    {
        List<DateSorter> wrappers = new List<DateSorter>();
        for (Task record : [/*query*/]) ...
        for (Note record : [/*query*/]) ...
        records = new List<SObject>();
        for (DateSorter wrapper : wrappers) records.add(wrapper.record);
    }
    public class DateSorter implements Comparable
    {
        //...
    }
}

Rename MyController to DateSorter. Then in your noteandtask_controller change wrappers.add(new noteandtask_controller(...)) to wrappers.add(new DateSorter(...)).

Change sortedRecords to be a List<SObject> property. Then after your sort call do:

sortedRecords = new List<SObject>();
for (DateSorter wrapper : wrappers) sortedRecords.add(wrapper.record);

Adrian, I am going back through the code to make sure I completely understand it. Can you explain a little further on:
wrappers.add(new myController(rec, 'Date_Activity_Logged__c'))

As of now how I am understanding it as: the for loop uses rec to look through the records1 list and then pull out any line item that has Date_Activity_Logged__c. I am unclear what the new myController does. And then I save these results into the list 'wrappers'.