You have only declared the Map and never initialized it before adding values into it. You have to initialize the IdValueMap in the start method or Constructor as below and you will not get the Exception.

IdValueMap = new Map<id , map<String, String>>();

PutAll only works on the ID field of an SObject. It is syntatic sugar for:

for(SObject record: someList)
    someMap.put(record.Id, record);

To use any other type of mapping, you would have to make your own for loop.

Such a for loop would look like:

Map<Id, Contract[0]> someMap = new Map<id, contract[0]>();

... load account ids here ...

for(Contract record: [SELECT Id, AccountId, random_field FROM Contract WHERE AccountId IN :someMap.keyset()]) {
    if(someMap.get(record.AccountId) == null) {
        someMap.put(record.AccountId, new Contract[0]);
    }
    someMap.get(record.AccountId).add(record);
}

In your specific case, I might consider using a subquery:

someMap.putAll([SELECT Id, (SELECT Id, random_field FROM Contracts) FROM Account WHERE Id IN :someMap.keySet()]);

You can access a list of contracts via:

for(Contract record: someMap.get(accountId).Contracts) ...

First, Maps are defined with two data types, such that we would express this in generic terms written with a unique letter for each data type involved: Map<T, U>, or as the documentation states: Map<T1, T2>. I prefer the classic nomenclature, but choose whichever you feel you understand better.

In your case, T is Id, and U is Map<T′, U′>. T′ and U′ are the type String. If you remember that, it should be easier to construct complicated types in the future:

Map< T ,            U          >
Map< Id, Map<   T′  ,   U′   > >
Map< Id, Map< String, String > > 

Second, to populate nested structures, you have to put them inside each other. In other words, before you can populate a value in the inner map, the outer map must have the object created first. To create most objects, we use the new keyword. One new is one new object.

When we create a new object, we call a constructor, which can take zero or more parameters to configure the initial state of the object. They are normal methods, which means we need to pass in any parameters, like we would any other method. new Map<Id, Map<String, String>>(), for example, constructs a new object with the compound data type Map<Id, Map<String, String>>.

So, to populate such a Map, we would do something like:

Map<Id, Map<String, String>> myMap = new Map<Id, Map<String, String>>();
myMap.put(obj.Id, new Map<String, String>());
myMap.get(obj.Id).put('value1','value2');

Note that put displaces the previous value if it exists, so we normally check first:

Map<String, String> myMapValue = myMap.get(obj.Id);
if(myMapValue == null) {
  myMapValue = new Map<String, String>();
  myMap.put(obj.Id, myMapValue);
}
myMapValue.put('value1','value2');

You can initialize a Map with the {} constructor format:

Map<Id, Map<String, String>> myMap = new Map<Id, Map<String, String>> {
  obj.Id => new Map<String, String> {
    'value1' => 'value2'
  }
};

Notice how there are two new keywords. We are still creating new objects, just placing one inside the other initially. The => operator simply means "key => value." This is the only use of => in Apex at this time.

Note that putAll is used to put a bunch of values inside the map at once. It requires that the parameter provided is the same type as U from our example above.

Map<Id, Map<String, String>> myMap = new Map<Id, Map<String, String>>();
Map<String, String> params = new Map<String, String>();
params.put('value1','value2');
myMap.put(obj.Id, new Map<String, String>());
myMap.get(obj.Id).putAll(params);

If you want to add a map onto existing map, use putAll() method.

finalMap.get('DETAILS').putAll(subDetails); 

It will add the entries of subDetails onto whatever Map finalMap contains aganist key 'DETAILS'.

you can modify your code like this.In this code I am creating a new instance for each map insert.

Map> result = new Map>(); List temp;

for(CustomObj__c i:customList){
    for(CustomObj__c j:customList2){
        if(j.id == i.id){
           temp = new list<string>();
           temp.add(j.Contact__r.Owner.Id);
           temp.add(j.Contact__r.Id);
           result.put(i.Deal__r.id, temp);
           break;
        }                
    }
}

Well, conveniently for us, the documentation is misleading/ambiguous and putAll does a true merge.

map<String,Integer> intsByKey = new map<String,Integer> 
   {'a' => 1, 'b' => 2};
intsByKey.putAll(new map<String,Integer> 
   {'c' => 3, 'd' => 4, 'a' => 10});

The value of intsByKey after the second statement is:

{a=10, b=2, c=3, d=4}

That is, putAll acts like addAll does for lists/sets

Props to Scott Hung's blog for saving me the trouble of writing a for loop

Taking time to try to understand the error message you're getting will help you understand how to move forward.

Although you have paraphrased the error and not included the stack trace (when asking about errors, you should never try to shorten it or paraphrase it. You don't know what the important part of the error is, and have a fair chance of leaving out vital information), it's pretty clear to experienced eyes that the issue is the following line

queriesList.get(queries) = new Map<Id,SObject>((List<SObject>)database.query(transformedQuery));

Explaining the error

The queriesList.get() part evaluates to a map, so that line of code ends up being
[A Map] = [A different Map];
which is not valid syntax (hence your error).

Variables can be assigned, but what you have here isn't a variable, it's an instance of a Map object.

Correcting that line of code

Instead of attempting to use the assignment operator, since you're working on an instance of a Map, you should be using one of the methods offered by the Map class.

The putAll() method can take a list of SObjects when the map is a Map<Id, SObject> (as you have), so that's what you should use here.

You also are doing some unnecessary casting (database.query() already returns a List<SObject>), so in the end you want that line to be something like
queriesList.get(queries).putAll(database.query(transformedQuery));

Other considerations

Your variable naming needs improvement. queriesList is a Map, not a List, and accQuery isn't a helpful description (it doesn't tell you what its purpose is)

Also, be aware that collections stored inside of collections are stored by reference. That means that right now, each query you store in your queriesList is storing the same map instance. If you have more than one query, the results for each individual query would appear in the map for every query string key.

At the very least, you would want to .clone() your accQuery map when you .put() a new query into the queriesList map.

Cloning gives you an independent copy, so that each map stored by the query template would only store the results of that one query.