Here are some possible, likely or very likely directions of immediate language change in a community of people with diverse monther tongues who use English as their medium of communication. As the question indicates, most of the members of the community speak English as a second language; very likely the varieties of English used in the community are not uniform, with some members approximating British English/RP because they had learned English in Europe, and others approximating General American.
We can safely assume that:
There will be an immediate and general loss of the aspiration of voiceless stops. Native English speakers pronounce
[kh] when they occur alone at the onset of a stressed syllable. (Slashes
// indicate a "broad" or phonemic transcription, brackets
 indicate a "narrow" or phonetic transcription.) Native speakers of most other European languages do not hear and cannot reproduce this pronounciantion reliably.
It is highly likely that there will be a loss of the English system of verbal aspects. English has an indefinite aspect and a continuous aspect; these don't map well to the verbal aspects of other languages, and many languages (such as the Romance family) don't have verbal aspects at all. It is probable that as speakers of English as a second language the members of the community have a rather imperfect grasp of the difference between the two verbal aspects of English, and they use the continuous aspect rarely if at all; it is very likely that by the third generation the continuous aspect will have dissapeared.
It is highly likely that the English preterite will be abandoned in favor of the present perfect; the latter has the advantage of being a clear formation, formally identical to the compound perfect of Romance languages and similar enough with the way Mandarin indicates that at action has taken place in the past. Hurray, one less principal verbal form to learn!
By the second or third generation everybody will speak a rhotic form of English; that is, they will pronounce words like "hard", "court" or "work" with an "r" sound,
/wɜrk/; forms like
/wɜːk/ will no longer be heard or understood. There will probably be a variety of realisations of
/r/ -- some will pronounce
[ɹ̠] (a postalveolar approximant, the common American "r"), others
[r] (a dental or alveolar trill, a common form or "r" in European languages other than English and French), ...
There will be a general simplification of the vocalic system, abandoning subtle distinctions which are hard to maintain by second-language speakers, moreover since the second-language English spoken by the members of the community is very likely not uniform in this respect; it is probable that the bewildering variety of English vowels will be simplified to a system approximating the cardinal vowels present in most languages, possibly with long and short, or maybe tense and lax varieties.
It is possible that the historical tendency of English to abandon grammatical gender will be taken to its ultimate conclusion, generalizing the pronoun "they" in the third person after the model of "you" in the second person, maybe retaining "it" (and the corresponding verbal form in
-s) for inanimate subjects.
It is likely that the synthetic English possesive in
's will be abandoned in favor of the more clear analytical possesive with
of. Most languages don't have two forms for the genitive/possesive, and the distinction between the two English forms is much too esoteric for second language speakers. (For my life, I wouldn't be able to tell what the distinction is; I generally try to parrot what I have hear or read, and in most technical writing I use the
's form sparingly if at all.)
The most dramatic changes will occur in the lexical sphere, as always. There is no way to prevent immediate change in the vocabulary, because with most members of the community there is simply too much variation, each speaker unconsciously attributing to English words the full set of connotations in their mother tongue.
It is quite likely that the immediate change will be to adopt an approximation of one of the varieties of controlled English, modeled on the controlled form of English used by the official regulations and technical manuals governing the space colony, most probably a form of the Simplified Technical English used by the aerospace and defense industries. STE simplifies English vocabulary with the aim of reducing ambiguities. For example, in STE the word "close" is always a verb, meaning to move two or more objects together or to operate a circuit breaker so that the circuit is established; the adjectival meaning of "close" in unrestricted English is assigned to the word "near". (A copy of the ASD-STE100 specification can be obtained from the official website after jumping through hoops, or, unofficially, from elsewhere.)
Since actual living linguistic communities don't like controlled natural languages at all, it is highly likely that there will be a phase of massive semantic shifts and vocabulary enrichment through derivation, composition, straight borrowing or calquing from the native languages of the first generation colonists.
How to convey linguistic change
Don't overdo it. Limit the direct representation of Nyoo Inglish to the minimum necessary to convey a flavor; don't attempt to write the whole book in it. Even a book such as A Clockwork Orange by Anthony Burgess tries to avoid overwhelming the reader with the Nadsat spoken by the characters.
For those sentences, phrases and words in New English / Nyoo Inglish you may want to use a form of (relatively) easy-to-read phonemic spelling such as
Axel Wijk's Regularized English; this will serve as "eye dialect", indicating that some new form of the language is used without actually compelling the reader to learn a new language.
You may also want to apply selectively some of the grammatical changes, either limited to the direct speech of the characters or not.
To get a flavor of a plausible non-English English, besides the above mentioned Clockwork Orange you may want to read Poul Anderson's Uncleftish Beholding, a short exposition of basic atomic (un-cleft-ish, a calque after Greek atomos, "uncut, indivisible") theory (be-hold-ing, a calque after Greek theôreô, "to look at, to behold"), written in a hypothetical "Anglish", that is, pure Germanic English without the massive Latin / Romance / Greek vocabulary.