I'd like to add to the (great) answers so far, based on the real life experience of being part of a multilingual group in several occasions.
While Joe's example would happen rather frequently in real life scenarios, I believe that the group will start using the most common / easiest to memorize or pronounce sounds from the collective vocabulary.
With the help of miming and drawing, this could go a long way in a relatively short time, and I believe that a group with the prospect of a long term forced stay with each other will have at least one smart person in it who will make sure that some time is dedicated to building a common language. In this scenario I imagine this leader figure to be smart enough to try and form a vocabulary that everyone can pronounce easily enough.
Using the example of the snake again, I imagine that in an alternative timeline where the word "aznat" hadn't been incorporated in the common language due to necessity, the group would gather together at some point of the day, possibly around lunch - snake stew? - and compare their terms for the creature...
*[I am using the transliteration conventions I am used to, apologies if this creates confusion to anyone. Also, most translations are Google based, I cannot guarantee they are correct. ? mean that I couldn't find a translation for a *specific language.]
সর্প (Sarpa) -> to which the English-speaker might add "serpent" as an alternative
term, happy to recognize a familiar sound
Most likely after the first times, they won't go around all 20 people for each term, but rather try different languages until someone recognized a familiar sound, and then work from there.
At this point I would expect the group to use a word starting with or including a sibilant sound, most likely ending up with either the Bengali term itself, or something like s*(r)p* (my guess is serpe/selpe/sepe).
This is somewhat similar to the process used for the creation of some artificial languages (I'm thinking about the semi-failed esperanto and europanto).
While general sounds might be very similar, I expect this group to either
1) shift towards a more limited number of sounds than their own languages, limiting the new pidgin to sounds accessible to everyone's mouth, or
2) to include words that are pronounced somewhat differently by different people with groups of sounds that can be used alternatively without changing the meaning of the word.
So in the example above I would expect the word for "snake" to be:
1) sepe (I am assuming here that all 20 people can pronounce the "s" sound in a manner that is common to everyone)
2) §e*pe (with § indicating s/sh/ts/..., and * being either omitted or something close to r/l)
While I believe case 2 to be initially more likely as it's simpler to agree on, with some attention to avoiding homophones, I would expect 1 to prevail in eventual future generations, or after a long period of time.
Some members of the group will realize that others are not as accustomed to the large number of vowel sounds, therefore the community will shift towards the use of a reduced number of vowels, pronounced with some differences, but likely rather easy to distinguish as A, E, I, O, U.
I don't think any of these languages has a more limited number of vowels or if their speakers would be likely unable to distinguish among these five.
Tones as used in mandarin will likely be ignored after a short time, as those familiar with them should notice how others are almost entirely unreceptive to them.
Very peculiar sounds - I am thinking clicks in the Khoisian languages as an example - might still be included in a simplified version that makes limited use of them, in short words.
With the number of possible phonemes being reduced, it will also be possible to settle on an alphabet common to all 20 members of the group. I believe that the chosen system will be the latin alphabet with possible modifications for extra sounds, being the most common within the group, and quite well suited for a language composed of simple sounds. It helps that most symbols are rather easy to discern and memorize, assuming uppercase letters being used.
...and some grammar
While most people will tend to follow their own grammar, as words for people, animals, objects, actions, and so on are agreed upon, I would expect a simple necessity driven-based grammar to prevail at first.
There would be no articles, the language would be mostly genderless, and singularity/plurality, gender, time, etc., would mostly be expressed through adjectives and adverbs.
The fist word in sentences would be a vocative (to attract the attention of the intended receiver of the message), the general argument of the message, or the subject; especially at first sentences may begin with a series of terms gradually specifying the subject, e.g.: "about food, today, midday: we now berry many gather".
Gestures will be very important at first, and while they won't be as necessary as time goes on, I expect the future of the group to look somewhat similar to communication in Italy: some concepts are expressed via sounds, some via gestures, often both go together. I will not elaborate further as Bill Blondeau already did so.
People from cultures with a more rare use of gestures will pick up on what other members of the small community do.