Vector of std::function with different signatures

You haven't said what you expect to be able to do with func2 after putting it in a vector with the wrong type.

You can easily use std::bind to put it in the vector if you know the arguments ahead of time:

const std::vector<std::function<void(std::string)>> functions
{
    func1,
    std::bind(func2, std::placeholders::_1, 5, 6)
};

Now functions[1]("foo") will call func2("foo", 5, 6), and will pass 5 and 6 to func2 every time.

Here's the same thing using a lambda instead of std::bind

const std::vector<std::function<void(std::string)>> functions
{
    func1,
    [=](const std::string& s){ func2(s, func2_arg1, func2_arg2); }
};

If you don't know the arguments yet, you can bind references to some variables:

int func2_arg1 = 5;
int func2_arg2 = 6;
const std::vector<std::function<void(std::string)>> functions
{
    func1,
    std::bind(func2, std::placeholders::_1, std::ref(func2_arg1), std::ref(func2_arg2))
};

Now functions[1]("foo") will call func2("foo", func2_arg1, func2_arg2), and you can assign new values to the integers to pass different arguments to func2.

And using a lambda function instead of std::bind

const std::vector<std::function<void(std::string)>> functions
{
    func1,
    [&](const std::string& s){ func2(s, func2_arg1, func2_arg2); }
};

This is pretty ugly though, as you need to keep the int variables around for as long as the callable object (the closure or the bind expression) referring to them exists.

What you want is possible through polymorphism. The idea is to create a class with a specific signature, which at runtime will call different methods. For example:

#include <iostream>
#include <functional>
#include <memory>
#include <vector>

void foo(int) {
    std::cout << "I'm foo!\n";
}

int bar(char, double) {
    std::cout << "I'm bar!\n";
}

class MyFunction {
    public:
        virtual ~MyFunction(){}

        virtual void operator()() = 0;
};

class MyFunctionA : public MyFunction {
    public:
        virtual void operator()() {
            foo(4);
        }
};

class MyFunctionB : public MyFunction {
    public:
        MyFunctionB(std::function<int(char,double)> f, char arg1, double arg2) : fun_(f), arg1_(arg1), arg2_(arg2) {} 

        virtual void operator()() {
            fun_(arg1_, arg2_);
        }
    private:
        std::function<int(char,double)> fun_;
        char arg1_;
        double arg2_;
};

int main() {
    using MyFunPtr = std::unique_ptr<MyFunction>;
    std::vector<MyFunPtr> v;

    v.emplace_back(new MyFunctionA());
    v.emplace_back(new MyFunctionB(bar, 'c', 3.4));

    for ( auto&& myfun : v ) {
        (*myfun)();
    }
    return 0;
}

You can make the derived classes as complicated as you need be, but since in the end they all have the same interface you will be able to call all of them.