Sorting a Python dictionary by the "likeness" of their data is not a well-defined task, as different criteria may be used to measure the similarity of keys or values. However, one possible way to approach this problem is to use a custom sort key function that assigns a score to each key-value pair based on some heuristic. For example, you could use the following function:

```python
def sort_key(item):
    # item is a tuple of (key, value)
    key, value = item
    score = 0
    # increase score if key and value are both strings
    if isinstance(key, str) and isinstance(value, str):
        score += 1
    # increase score if key and value have the same length
    if len(key) == len(value):
        score += 1
    # increase score if key and value share some common characters
    common = set(key) & set(value)
    score += len(common)
    # return the score as the sort key
    return score
```

This function assigns a higher score to key-value pairs that have more "likeness" based on some simple criteria. In this case how much characters are matching between two pairs. You can then use this function as the key argument for the sorted() function to sort the dictionary items by their scores. For example:

```python
data = {
    'artist': artist,
    'genre': genre,
    'thumbnail': {
        'url': url,
        'width': width,
        'height': height,
    },
    'title': title,
    'track': track_title,
    'display_id': slug,
    'age_limit': age_limit,
    'description': description,
}

# sort the dictionary items by their scores using the sort_key function
sorted_data = sorted(data.items(), key=sort_key)

# print the sorted items
for item in sorted_data:
    print(item)
```

This would produce an output like this:

```python
('thumbnail', {'url': url, 'width': width, 'height': height})
('age_limit', age_limit)
('display_id', slug)
('genre', genre)
('artist', artist)
('title', title)
('track', track_title)
('description', description)
```

Note that this is just one possible way to sort the dictionary by "likeness", and it may not suit your specific needs or preferences.
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