Are there any chengyu or xiehouyu that only mean their literal meaning? Most chengyu and xiehouyu have a literal meaning and a figurative meaning.

Take 鸡飞狗跳 for instance, it literally means [the] chicken[s] fly [and the] dog[s] jump, figuratively it stands for chaos and confusion.

Or 孔夫子搬家——净是书 literally means Confucius moves house —— there's nothing but books, but figuratively books sounds the same as loss or lose (输) giving the meaning of always losing.

With these xiehouyu and chengyu the emphasis is always placed on the figurative meaning and not the literal meaning.

Are there chengyu that only have a literal meaning with no figurative meaning at all?

Perhaps 泥菩萨过河 would count as one - it seems that its literal meaning already does the trick of conveying what it wants to say without any other necessary added meaning.

Are there others?
I think all chengyus should have their figurative meanings. 

xiehouyu  usually has two kinds: 


  
  逻辑推理式 // logical type, For example, 哑巴吃黄连, 有苦说不出.
  谐音 // homophony, For example, 外甥打灯笼, 照旧(舅)
  


泥菩萨过河 should fall into logical type. So, there are lots of that type if you go Baidu. 

Couple of links for your reference:


  逻辑推理式
  
  谐音