You can contact the witnesses any way you wish and should find out beforehand what they intend to say, it may be easiest if you travel to the hearing with your witnesses. If any witness does not wish to come, but you believe they have helpful information to contribute ask the court to contact them, as a courtesy inform the tribunal the number of witnesses who will be attending. Unfortunately they may not be paid by the employer and court and may look to you for recompense, on occasions a witness may not wish to comment on their employer’s behaviour from fear of repercussions, also remember rules over evidence are relaxed at a tribunal and hearsay may be admitted.
Your company’s lawyer may be asking how long you were unemployed to calculate what the court may order you to be paid, together with their fees which the employer will have to pay to see if it is worth your employer making you an offer to settle.
Provide the tribunal with any information they request, they may require you to give a written statement of your position and what your witnesses will say, but your witnesses should still attend. As you probably know there is a lot of bluff in the law and many tribunal hearings are settled before the actual hearing, if you have a good case do not give in and only settle if the offer is fair.
Good luck.