How to make a tenseless sentence?
There are two things to be cleared:


To say a language is tenseless means it does not have a grammatical category of tense (e.g. word morphology, auxiliary verbs and tense particles in English). Chinese sentences do refer to time but by using lexical words such as adverbs and verbs, with a combination of aspect, mood and other language elements.
The examples in your question are not complete sentences. They are sentence fragments, such as clauses and phrases, that may or may not contain time references. When they are used in a complete sentence, in most of the cases, a time reference will exist in one form or another.





  我吃完饭 sounds tenseless


That's true, because it is a sentence fragment without any time reference. To make a complete sentence with it there are two options:


Add 了 particle: 



  我吃完饭了。I am done eating (now).


了 is a complicated matter and doesn't indicate tense by itself. But in this sentence, 完 (complete; done) and 了 (state change marker) together form a verb+完+[object]+了 phrase, which is a clear signal for present perfect tense. 


Use this phrase as a adverbial clause: 



  我吃完饭，就去写作业。I'll do my homework after I'm done eating.


The lack of time reference in either clause (吃完饭, 去写作业) suggests neither has happened yet, so it's a statement of plan, which maps to simple present tense in English. 

The ambiguity though, is we couldn't tell if the speaker has already started eating, but the same can be said for the English version.



Now back to the subject of the question, how to make a tenseless sentence? Strictly speaking, given how grammatical tense is defined (see #1 in at the beginning of this answer), all Chinese sentences are tenseless and the language is a tenseless language. 

I think what you really want to know is 'what are some common sentences with ambiguous time reference'. After some thought, I couldn't think of any real sentences in their actual contexts like that. I couldn't think of any sentence or even clause that has ambiguous time reference while its English counterpart doesn't, either.

For example, the clauses 我吃完饭 and 我吃饭 sound 'tenseless', the same can be said for 'I finish eating' and 'I eat'. Grammatically they are simple present tense, but as sentences they don't make any sense. 

So if you want to create sentences with ambiguous time reference, simply omit any verbs, adverbs or other language elements that refer to time, but they sound either incomplete or unnatural.