Having problems with creating menu in C using do..while and if..else statement

The problem is simple: the terminal is line buffered: you must press enter for the input to become available to your program, the first scanf("%c", &choice) retrieves the character typed and the second call retrieves the linefeed ('\n') that was generated by the enter key.

There are multiple ways to avoid this problem. You can add a space in the scanf format before the %c: scanf(" %c", &choice); or you can read characters after the first until you get a '\n'.

Note that you must check the return value of scanf to avoid undefined behavior if the user enters an end of file. It is also advisable to avoid global variables: the function menu() should return the choice specified. Using a switch statement is also more idiomatic for this.

Here is a corrected version:

#include <stdio.h>

int menu(void);
void choice1(void);
void choice2(void);
void choice3(void);

int main(void) {
    int ch;
    for (;;) {
        switch (ch = menu()) {
        case '1':  choice1();  continue;
        case '2':  choice2();  continue;
        case '3':  choice3();  continue;
        case '4':
        case EOF:  break;
        default:   printf("Invalid character %c\n", ch);  continue;
        }
        break;
    }
    return 0;
}

int menu(void) {
    char choice;

    printf("\nMenu:\n\n");
    printf("1) Choice 1.\n");
    printf("2) Choice 2.\n");
    printf("3) Choice 3.\n");
    printf("Choose any of the above, or enter 4 to quit.\n\n");
    if (scanf(" %c", &choice) == 1)
        return choice;
    else
        return EOF;
}

void choice1(void) {
    printf("\nChoice 1\n");
}

void choice2(void) {
    printf("\nChoice 2\n");
}

void choice3(void) {
    printf("\nChoice 3\n");
}

As already mentioned in other answers the problem is the newline character.

When you press 1 followed by enter, you'll get two chars, i.e. 1 and \n. So your loop runs twice and prints Invalid character when \n is processed.

Here is an alternative solution for your problem. Just add a space before %c.

scanf(" %c", &choice);

This works because the space will match any number of white-space characters and thereby match the \n and remove it.

From the man page:

A sequence of white-space characters (space, tab, newline, etc.......). This directive matches any amount of white space, including none, in the input.

Additional comments

You should always check the value returned by scanf to make sure you read the correct number of values.

 if (scanf(" %c", &choice) != 1)
 {
     // Add error handling ....
     // For instance you could terminate the program like
     exit(1);
 } 

In your program choice is a global variable. In general global variables should be avoid if possible. In your case you could make choice a local variable in main and let menu return a char. Like:

// char choice;  Remove global variable

int main() {
    char choice; // Add local variable
    do {
        choice = menu();  // Assign to local variable
        .....
}

char menu(void) {    // Make the function return a char
    char choice;     // Add local variable

    printf("\nMenu:\n\n");
    printf("1) Choice 1.\n");
    printf("2) Choice 2.\n");
    printf("3) Choice 3.\n");
    printf("Choose any of the above, or enter 4 to quit.\n\n");
    if (scanf("%c", &choice) != 1) exit(1); // Assign to local variable
                                            // On failure -> exit

    return choice;  // Return value of local variable
}

You can write scanf(" %c",&choice); (with whitespace) instead of scanf("%c",&choice);

When I try to run it, by putting the number 1, 2, 3, the output came out but after that the function menu() and also the line "Invalid character." came out.

It's happening because of the new line character you press after each number. It's itself a character and loop is iterated one more time for this. As it is an invalid character, that's why "Invalid character." is showing.

Try using getchar() after scanf().

Edit: fixed my previous while loop which may exit incorrectedly:

#include <stdio.h>
int main() {
  int choice;
  printf("Menu:\n\n");
  printf("1) Choice 1.\n");
  printf("2) Choice 2.\n");
  printf("2) Choice 3.\n");
  printf("Choose any of the above, or enter 4 to quit.\n\n");
  while (1) {
    char c = scanf("%d",&choice);
    if (c == EOF || choice == 4) break;
    if (choice == 1 || choice == 2 || choice == 3) {
      printf("Choice %d.\n", choice);
    } else {
      printf("Invalid character.\n");
    }
  }
  return 0;
}

You can use function if you want, but not necessary in this case. You need to understand how many times your loop actually runs and compare it to that you expect.

My previous code:

#include <stdio.h>
int main() {
  int choice;
  printf("Menu:\n\n");
  printf("1) Choice 1.\n");
  printf("2) Choice 2.\n");
  printf("2) Choice 3.\n");
  printf("Choose any of the above, or enter 4 to quit.\n\n");
  while (scanf("%d", &choice) && choice != 4) {
    if (choice == 1 || choice == 2 || choice == 3) {
      printf("Choice %d.\n", choice);
    } else {
      printf("Invalid character.\n");
    }
  }
  return 0;
}